UC-NRLF 


$B    a05    27T 


THE 


DIFFUSION  OF  GASES  THROUGH  LIQUIDS 
AND  ALLIED  EXPERIMENTS 


By  carl  BARUS 

Hazard  Professor  of  Physics  and  Dean  of  the  Graduate  Department 
in  Brown  University 


WASHINGTON,  D.  C. 

Published  by  the  Carnegie  Institution  of  Washington 

1913 


THE 

DIFFUSION  OF  GASES  THROUGH  LIQUIDS 

AND  ALLIED  EXPERIMENTS 


By  carl  BARUS 

Hazard  Professor  oj  Physics  and  Dean  of  the  Graduate  Department 
in  Brown  University 


DUIVERSITY  OF  CALIFORNIA 

LIBRARY 

BRANCH  OF  THE 
COLLEGE  OF  AGRICULTURE 

WASHINGTON,  D.  C. 

Published  by  the  Carnegie  Institution  of  Washington 

1913 


CARNEGIE  INSTITUTION  OF  WASHINGTON 
Publication  No.  i86 


PRESS  OF  GIBSON  BROTHERS 
WASHINGTON,  D.  C. 


PREFACE. 


Observing  that  the  Cartesian  diver  used  in  my  lectures  since  1895  grew 
heavier  from  year  to  year,  I  resolved  in  1900  to  make  definite  measurements 
of  the  rate  of  loss  of  buoyancy,  believing  that  these  would  be  fruitful ;  they 
would  bear  directly  on  the  coefficient  of  diffusion  of  the  imprisoned  gas 
through  the  liquid  in  which  the  diver  is  floating;  it  would  be  easily  possible 
to  vary  the  liquids  and  gases,  within  and  without,  under  conditions  of  a 
determinable  diffusion  gradient.  Ultimately  the  transfer  of  single  mole- 
cules of  a  gas  through  the  intermolecular  pores  of  the  liquid  is  in  question, 
so  that  the  experiment  might  throw  definite  light  on  the  size  of  physical 
pores  and  on  the  other  molecular  relations  involved. 

The  experiments  in  Chapter  I,  made  during  a  period  of  eleven  years,  with 
an  ordinary  glass  balloon-shaped  Cartesian  diver  with  a  small  aperture, 
culminated  in  a  plausible  value  of  the  diffusion  coefficient  {i.  e.,  grams  of 
gas  or  standard  volume  of  gas  transpiring  per  second  across  an  orthogonal 
square  centimeter,  in  case  of  a  unit  pressure  gradient)  of  the  imprisoned  air 
through  water,  together  with  suggestive  relations  of  the  mean  viscosity  of 
the  imaginary  medium  within  the  molecular  pores  of  the  liquid  through 
which  a  single  molecule  of  the  gas  virtually  transpires.  The  investigation 
was  therefore  taken  up  on  a  more  extended  scale,  for  different  pairs  of  gases. 

In  Chapter  II  the  diver  is  modified  in  form  and  the  endeavor  is  made  to 
obtain  equal  areas  in  the  section  of  the  cylindrical  swimmer  and  the  annular 
space  without,  in  order  to  conform  more  closely  to  the  equation  of  diffusion. 
The  theory  of  the  phenomenon  and  the  errors  involved  are  discussed.  It 
appears  that,  even  for  mixed  gases,  the  volumes  diffusing  (if  not  the  masses) 
are  fully  determinable.  The  accuracy  essentially  depends  on  the  measure- 
ment of  absolute  temperature  and  of  barometric  pressure  and  should  there- 
fore be  of  an  order  below  1/2730  per  0.1°  C.  or  1/7600  per  o.i  centimeter  of 
mercury.  As  the  masses  of  gas  contained  are  as  a  rule  much  less  than  io~^ 
gram,  even  in  case  of  air,  the  weight  less  than  0.000004  gram  is  determinable, 
showing  the  remarkable  sensitiveness  of  the  method.  Moreover,  in  the  region 
of  constant  temperature,  the  limit  of  sensitiveness  is  immensely  greater. 

In  order  to  elucidate  the  phenomenon,  experiments  were  begun  with  the 
transpiration  of  imprisoned  hydrogen  into  air,  in  which  the  resultant  diffu- 
sion is  always  unidirectional,  outward  from  the  diver.  Initially  rates  as 
large  as  5  mg.  per  day  were  obtained,  which  eventually  decreased  to  a  con- 
stant value,  equivalent  to  a  fixed  diffusion  coefficient  which  indicated  the 
diffusion  of  air  only.  The  case  of  air  into  air  through  water  showed  a 
definite  mean  rate  throughout  the  two  or  three  months  of  observation ;  but 
the  daily  march  of  the  loss  by  diffusion  was  remarkably  irregular,  a  result 
finally  referred  to  the  change  of  solubility  of  the  gases  in  water  with  tern- 


4^1^ 


n  PREFACE. 

perature.  The  result  of  this  is  absorption  and  release  of  gas  as  temperature 
falls  or  rises,  respectively,  during  the  occurrence  of  the  otherwise  steady- 
diffusion.  In  the  long  series  the  temperature  effect  was  eliminated  by  the 
method  of  least  squares. 

Much  more  striking  were  the  phenomena  encountered  in  endeavoring  to 
find  the  coefficient  of  diffusion  of  hydrogen  through  water  into  hydrogen — in 
which,  however,  the  ultimate  daily  loss  of  weight  of  the  diver  became  con- 
stant, corresponding  to  the  diffusion  coefficient  of  hydrogen  alone.  Referred 
to  molecular  conditions,  the  molecule  can  be  regarded  as  moving  through  a 
medium  about  15  times  as  viscous  as  ordinary  hydrogen,  whereas  in  case  of 
air  the  medium  would  be  about  13  times  as  viscous  as  air.  The  daily  march 
of  results  in  the  hydrogen  observations  was  most  striking,  inasmuch  as  the 
diver  first  lost  weight  at  an  initially  enormous  rate  for  two  days,  then 
rapidly  gained  weight  at  a  decreasing  rate  during  the  ensuing  ten  days,  and 
thereafter  assumed  the  steady  rate  of  loss  for  months.  Changes  of  this 
nature  are,  as  a  rule,  abrupt.  It  was  found  that  a  similar  doubly  inflected 
progression  of  results  usually  occurs  unless  all  manipulations  at  the  outset 
are  conducted  not  in  air,  but  in  a  medium  of  hydrogen,  or  in  general  of  the 
identical  gas  within  the  diver.  Otherwise  the  imprisoned  gas  is  at  once  con- 
taminated by  diffusion  of  the  surrounding  gas  into  it. 

It  is  not,  perhaps,  fully  appreciated  by  chemists  that  gases,  otherwise 
pure,  if  stored  over  water,  at  once  lose  purity  in  consequence  of  air  by 
diffusion.  In  fact  a  gas.  A,  in  the  swimmer,  in  presence  of  gases,  B,  C, etc., 
can  not  escape  by  diffusion  until  the  sum  of  the  partial  pressures,  B,  C,  etc., 
is  equal  to  or  greater  than  the  pressure  equivalent  of  the  head  of  water  under 
which  the  gas  A  is  submerged.  Before  that  the  gas  of  the  environment  will 
diffuse  into  the  diver  against  the  hydrostatic  pressure  of  the  head  of  water, 
i.  e.,  apparently  up  hill.  The  same  explanation  accounts  for  the  enormous 
inflation  of  the  microscopic  air  bubbles,  for  instance,  in  the  liquid,  when  the 
surrounding  atmosphere  is  some  other  gas,  like  hydrogen;  also  for  the 
bubbles  which  still  appear  and  grow  at  rough  points  of  a  surface  after  the 
effervescence  of  a  compound  gas  has  ceased. 

Other  diffusion  experiments,  air  into  hydrogen,  oxygen  into  hydrogen, 
hydrogen  into  air,  etc.,  were  eventually  pursued  through  months  and  com- 
pleted in  a  similar  manner  and  with  similar  results.  The  graphs  obtained 
are  throughout  striking.  It  is  feasible  to  derive  the  differential  equation 
for  these  phenomena,  but,  as  might  be  expected  from  the  complications  in 
question,  it  could  not  be  integrated.  Finally,  it  is  interesting  to  note  that 
if  the  diffusion  coefficients  are  given,  the  densities  of  the  gases  diffusing  at  a 
constant  rate  may  be  computed;  or,  from  another  point  of  view,  the  degree 
of  purity  of  the  gas  so  diffusing  may  be  ascertained. 

The  sensitiveness  of  weighing  in  case  of  the  Cartesian  diver,  where  the 
whole  apparatus  is  quite  submerged  in  water  or  some  other  liquid  and  capil- 
lary forces  are  out  of  the  question,  naturally  suggested  the  application  of  this 
method  for  the  measurement  of  high  potentials  in  case  of  the  absolute  elec- 


PREFACE.  in 

trometer.  For  this  purpose  the  whole  condenser,  as  described  in  Chapter 
III,  is  submerged  in  a  clear  non-conducting  paraffin  oil,  while  the  mov- 
able disk  of  the  electrometer  is  floated  on  a  Cartesian  diver,  or  the  circular 
top  of  a  cylindrical  diver  is  itself  the  disk.  The  difference  of  weight  of  a 
charged  and  uncharged  condenser  is  determinable,  the  former  in  view  of  the 
electrical  pressures  being  less.  It  may  then  be  shown  that  the  absolute 
difference  of  potential  of  the  plates,  cat.  par.,  varies  as  their  distance  apart 
and  as  the  square  root  of  the  difference  of  the  manometer  pressures  which 
are  just  compatible  with  flotation,  in  the  case  of  the  charged  and  uncharged 
condensers,  respectively.  By  keeping  the  difference  in  question  constant, 
potentials  may  be  absolutely  measured  in  terms  of  the  distance  apart  of  the 
plates  from  about  50  volts  to  indefinitely  large  magnitudes. 

These  experiments  suggested  a  variety  of  other  methods.  Thus  the  disk 
of  the  absolute  electrometer,  now  kept  in  air,  was  buoyed  up  and  held  in 
place  on  a  hydrometer,  with  its  body  submerged  in  water  or  in  oil,  where  the 
capillary  forces  are  small.  Particularly  interesting  results  were  obtained 
when  the  hydrometer  was  a  very  thin,  straight  aluminum  tube,  at  right 
angles  to  the  light  aluminum  plate  of  the  condenser,  the  aluminum  tube 
being  submerged  in  a  glass  tube  which  is  one  shank  of  a  U-tube.  It  is  shown 
that  for  a  difference  of  potential  of  the  disks  (supposed  horizontal), not  too 
large,  there  is  a  stable  and  an  unstable  position  of  the  movable  disk,  the 
former  below  the  latter.  The  disk  therefore  rises  from  its  fiducial  position  in 
the  uncharged  condenser  to  a  definite  height.  As  the  difference  of  potential 
increases  this  height  increases  until  at  a  transitional  height  both  stable  and 
unstable  positions  coincide.  For  greater  differences  of  potential  the  disk 
passes  without  intermission  from  the  lower  plate  (guard  ring)  to  the  upper 
plate  of  the  condenser.  If  the  difference  of  potential  is  constant,  the  same 
phenomena  may  be  evoked  on  diminishing  the  distance  apart  of  the  plates 
of  the  condenser,  by  lowering  the  upper  plate  on  a  micrometer  screw. 
Potentials  may  then  be  absolutely  measured  in  terms  of  the  distance  apart 
of  the  plates  at  which  the  continuous  rise  of  the  disk  first  occurs. 

Other  similar  experiments  were  devised,  such  as  the  treatment  of  Cou- 
lomb's law  when  one  of  the  repelling  bodies  is  a  Cartesian  diver,  the  repe- 
tition of  Mayer's  experiments  when  the  charged  metallic  bodies  are  floated 
in  oil  in  a  charged  guard  ring,  etc. 

Finally,  the  experience  gained  in  Chapter  III,  in  relation  to  methods  of 
filling  the  diver  with  a  gas  in  an  environment  of  the  same  gas,  a  condition 
rigorously  necessary  if  the  gases  are  to  remain  adequately  pure  for  diffusion 
measurements,  suggested  the  further  development  of  certain  of  the  experi- 
ments in  Chapter  II.  These  are  given  in  Chapter  IV.  In  addition  to  this, 
the  chapter  begins  the  work  of  treating  the  diffusion  of  gases  through  solu- 
tions systematically  and  at  length.  It  contains  the  effect  produced  on  the 
diffusion  coefficient  of  air  by  dissolving  in  water  different  quantities  of  KCl, 
NaCl,  CaCla,  BaClg,  SrClz,  K2SO4,  Na2S04,  FeCl,,  AICI3,  etc.  The  purpose 
here  is  at  present  chiefly  the  gathering  of  data.     The  work  is  so  laborious. 


IV  PREFACB. 

SO  essentially  slow,  and  so  full  of  pitfalls,  that  the  serious  attempt  to  draw 
conclusions  from  the  data  in  hand  must  be  deferred.  It  appears,  however, 
that  in  all  cases  the  physical  pores  of  a  solvent  like  water  are  effectively 
closed  by  a  solute,  but  that  the  amount  of  closure  is  dependent  on  the  char- 
acter of  the  salt  and  the  density  of  the  solution  in  a  way  not  to  be  easily 
surveyed.  Thus  a  dilute  solution  may  show  greater  cloture  than  a  concen- 
trated solution  of  the  same  salt,  due  no  doubt  to  the  formation  of  hydrates 
effective  in  this  respect.  It  appears  also  that  the  diJBfusion  coefficients 
obtained  from  direct  manometer  experiments  in  the  lapse  of  years  are  not 
at  once  comparable  with  the  results  for  the  divers  in  the  lapse  of  months, 
all  of  which  disparities  will  need  long-continued  observation. 

My  thanks  are  as  usual  due  to  Miss  Ada  I.  Burton  for  most  efficient 
assistance  through  the  whole  of  this  work,  both  in  its  experimental  and 
editorial  parts.  The  data  of  Chapter  IV,  requiring  a  high  order  of  patience 
and  accuracy,  both  as  to  observations  and  computation,  have  been  largely 
contributed  by  her. 

Cari,  Barus. 

Brown  University, 

Providence,  Rhode  Island. 


CONTENTS. 


Chapter  I. — The  Transpiration  of  Air  through  a  Partition  of  Water. 

PACE. 

1 .  Molecular  transpiration  of  a  gas i 

2.  Apparatus.     Fig.  i i 

3.  Barometer i 

4.  Equations.     Manipulation.     Fig.  2 2 

5.  Data.     Table  i 2 

6.  Conditions  of  flow 3 

7.  Coefficients  of  transpiration 4 

8.  Values  of  the  coefficients 5 

9.  Conclusion 6 

Chapter  II. — The  Transpiration  of  the  Systems  Air-Air,  Hydrogen- 
Hydrogen,  Air-Hydrogen,  Hydrogen-Air,  etc.,  through  Water. 

ID.  Introductory.     Apparatus.     Figs.  3  and  4 7 

11.  Imprisoned  hydrogen  diffusing  into  free  air.      Preliminary  data.      Fig.  5, 

table  2 8 

12.  Continued.     Coefficients  depending  upon  water  heads  only 10 

13.  Continued.     Apparent  factional  resistance  per  molecule.     Virtual  viscosity.  11 

14.  Continued.     Transpiration  depending  upon  barometric  pressure 12 

15.  Continued.     Influx  of  air  into  the  imprisoned  hydrogen 13 

16.  Continued.     Coefficients  depending  on  diffusion  gradients.     Transpiration..  13 

1 7.  Continued.     Flotation 14 

18.  Continued.     Potential  energy  of  the  gas  mixture 17 

19.  Transpiration  of  air  into  air  through  water.     Fig.  6;  table  3 18 

20.  Transpiration  of  hydrogen  into  hydrogen  through  water.     Fig.  7;  table  4. . .  22 

2 1 .  Transpiration  of  impr  isoned  air  into  hydrogen  through  water.     Fig.  8 ;  table  5 .  25 

22.  Transpu-ation  of  oxygen  into  hydrogen  through  water.     Fig.  9;  table  6 28 

23.  Transpiration  of  hydrogen  into  air  through  water.     Fig.  10;  table  7 31 

24.  Correction  for  density  of  the  glass.     Table  8 32 

25.  Summary.     Relatively  slow  diffusion  of  mixed  gases.     Tables  9  and  10 33 

Chapter  III. — Hydrostatic  Methods  for  the  Absolute  Eusctrometry 
OF  High  Potentials. 

I.     Hydrometer  Methods. 

26.  Introduction 39 

27.  Absolute  electrometer.     Figs.  11  a,  jib,  12,  13 39 

28.  Equations  for  the  tubular  float 42 

29.  Constants  of  the  tubular  float.     Fig.  14 43 

30.  Constants  of  the  conical  float  (capsule) 44 

31.  Experiments  with  the  tubular  float.     Table  ii 45 

II.    Absolute  Electrometry  by  Aid  of  the  Cartesian  Diver. 

32.  Introductory 46 

33.  Apparatus.     Fig.  15 47 

34.  Equations.     Table  12 48 

35.  Measurements.     Tables  13,  14 50 

Chapter  IV. — The  Diffusion  of  Gases  through  Solutions  and 
Other  Liquids. 

36.  Purpose 55 

37.  Apparatus.     Fig.  16;  table  15 55 

38.  Equations 57 

39.  Diff^usion  of  air  into  air  through  water.     Fig.  17;  table  16 58 

40.  The  same,  continued.     Fig.  18;  table  17 61 

41.  Diffusion  of  air  into  air  through  water;  further  experiments.     Figs.  19  a,  b,  c, 

20;  tables  18,  19,  20,  21,  22 62 

V 


VI  CONTENTS. 

PAOB. 

42.  Diffusion  of  hydrogen  into  hydrogen  through  water.     Fig.  21 ;  table  23 66 

43.  Diffusion  of  air  into  air  through  KCl  solution.     Fig.  22;  table  24 67 

44.  The  same,  continued.     Fig.  23 ;  table  25 69 

45.  The  same,  continued.     Fig  24;  table  26 70 

46.  The  same,  continued.     Fig.  25 ;  table  27 71 

47.  Diffusion  of  air  into  air  through  NaCl  solution.     Fig.  26  a;  table  28 72 

48.  The  same,  continued.     Fig.  26  b;  table  29 73 

49i  50,  51.  52.  Diffusion  of  air  into  air  through  CaCl,  solution.     Figs.  27,  28  A, 

28 B,  29;  tables  30,  31.  32,  33 73 

53.  54.  55-  Diffusion  of  air  into  air  through  BaClj  solution.     Figs.  30,  31;  tables 

34, 35.  36 76 

56,  57,  58.  Diffusion  of  air  into  air  through  KjSO<  solution.     Figs.  32,  33;  tables 

37.  38,  39 78 

59,6o.DiffusionofairintoairthroughNa2S04Solution.  Figs.34A,34B;  tables  40,41  80 

61,62.  Diffusion  of  air  into  air  through  FeClj  solution.  Figs.  35  A,  35  b;  tables  42, 43.  81 

63.  Diffusion  of  air  into  air  through  AlClj  solution.     Fig  36;  table  44 83 

64.  Diffusion  of  a  gas  through  a  manometer  tube.     Fig.  37;  table  45 83 

65.  Summary.     Fig.  38 ;  table  46 85 


THE  DIFFUSION  OF  GASES  THROUGH  LIQUIDS  AND 
ALLIED  EXPERIMENTS 


By  carl  BARUS 

Hazard  Professor  of  Physics  and  Dean  of  the  Graduate  Department 
in  Brown  University 


CHAPTER  I. 


THE  TRANSPIRATION  OF  AIR  THROUGH  A  PARTITION  OF  WATER. 

1.  Molecular  Transpiration  of  a  Gas. — Ever  since  1895  I  have  observed 
that  the  Cartesian  diver  used  in  my  lectures  grew  regularly  heavier  from 
year  to  year.  The  possibility  of  such  an  occurrence  is  at  hand;  for  the 
imprisoned  air  is  under  a  slight  pressure-excess  as  compared  with  the 
external  atmospheric  air.  But  this  pressure  gradient  is  apparently  so  insig- 
nificant as  compared  with  the  long  column  of  water  through  which  the 
flow  must  take  place  that  opportunities  of  obtaining  quantitative  evidence 
in  favor  of  such  transpiration  seem  remote.  If,  however,  this  evidence  is 
here  actually  forthcoming,  then  the  experiment  is  of  unusual  interest,  as  it 
will  probably  indicate  the  nature  of  the  passage  of  a  gas  molecularly  through 
the  intermolecular  pores  of  a  liquid.  It  should  be  possible,  for  instance,  to 
obtain  comparisons  between  the  dimensions  of  the  molecules  transferred 
and  the  channels  of  transfer  involved. 

2.  Apparatus. — Hence  on  February  27,  1900,  I  made  a  series  of  definite 
experiments*  sufficiently  sensitive  so  that  in  the  lapse  of  years  one  might 
expect  to  obtain  an  issue.  The  swimmer  was  a  small,  light,  balloon-shaped 
glass  vessel,  vd,  fig.  i,  unfortunately  with  a  very 

narrow  mouth  2  mm.  in  diameter  at  d,  in  the  long 
column  of  water  A .  The  small  opening,  however, 
gave  assurance  that  the  air  would  not  be  acci- 
dentally spilled  in  the  intervening  years.  For  this 
reason  it  was  temporarily  retained,  the  purpose 
being  that  of  getting  a  safe  estimate  of  the  con- 
ditions under  which  flow  takes  place. 

In  fig.  I ,  aft  is  a  rubber  hose  filled  with  water, 
terminating  in  the  receiver  R.  Here  the  lower 
level  of  water  may  be  read  off.  Moreover,  R  is 
provided  with  an  open  hose  C,  through  which  pres- 
sure or  suction  may  be  applied  by  the  mouth,  for 
the  purpose  of  raising  or  lowering  the  swimmer,  vd,  in  the  column  A.  In 
this  way  constancy  of  temperature  is  secured  throughout  the  column. 

3.  Barometer. — The  apparatus  is  obviously  useful  for  ordinary  baro- 
metric purposes,  and  provided  the  temperature,  /,  of  the  air  at  v  is  known 
to  0.025°  C,  the  barometric  height  should  be  determinable  as  far  as  o.i  mm. 
Apart  from  this  the  sensitiveness  of  the  apparatus  is  surprising.  Great  care 
must  be  taken  to  avoid  adiabatic  changes  of  temperature,  so  that  slow 
manipulation  is  essential.  These  and  other  precautions  were  pointed  out 
in  the  original  paper.  The  apparatus  labors  under  one  fundamental  diffi- 
culty, as  the  diffusion  of  a  compound  gas  like  air  is  a  complicated  discrep- 


FiG.  I. — Cartesian  diver  ad- 
justed for  diffusion  meas- 
urement. 


*Am.  Joum.  Sci.,  ix,  1900,  pp.  397-400. 


2  THE   DIFFUSION  OF  GASES  THROUGH 

ancy  which  will  be  felt  in  the  lapse  of  time.  The  question  will  be  discussed 
in  the  next  chapter. 

4.  Equations.  Manipulation. — Let  A  be  the  difference  of  level  of  the  impris- 
oned water  and  the  free  surface  in  the  reservoir  R.  Then  it  follows  easily  that 

""^""p^      gM{i+m/M)-pJp,  ^'^ 

where  H  is  the  corrected  height  of  the  barometer  (from  which  the  mercury 
head  equivalent  to  the  vapor  pressure  of  water  is  to  be  deducted),  p„ ,  p^,,  pg, 
the  densities  of  mercury  (o°  C),  water  (^°  C),  and  glass, 
respectively,  m  the  mass  of  the  imprisoned  air  at  v,  R  its 
gas  constant,  and  t  =  /  +  273°  its  absolute  temperature. 
V;-[yp^^^  i"  ^  ^^  ^^  mass  of  the  glass  of  the  swimmer  and  g  the  acceler- 
ation of  gravity. 

The  equilibrium  position  of  the  swimmer  is  unstable. 
To  find  it  R  may  be  raised  and  lowered  for  a  fixed  level  of 
the  swimmer;  or  R  may  be  clamped  and  the  proper  level  of 
Fig.  2. — Cylin-  the  swimmer  determined  by  suction  and  release  at  C.  The 
dropping  of  the  swimmer  throughout  the  column  of  water 
may  occasion  adiabatic  change  of  temperature  of  0,23°.  It  was  my  practice 
in  the  present  experiments  to  use  the  latter  method  and  to  indicate  the 
equilibrium  position  of  the  swimmer  by  an  elastic  steel  ring  encircling  A . 
In  this  way  the  correct  level  may  be  found  to  about  i  mm.  and  afterwards 
read  off  on  the  cathetometer. 

After  making  the  observations,  the  hose  ah  is  to  be  separated  at  a,  so  that 
the  swimmer  falls  to  a  support  some  distance  above  the  bottom,  admitting 
of  free  passage  for  diffusion.  Clearly  this  diffusion  is  due  to  the  difference 
of  level,  h",  between  the  water  in  v  and  at  the  free  surface  of  the  liquid 
(see  fig.  2).  Increase  of  barometric  pressure  has  no  differential  effect.  A 
large  head  h'",  however,  means  a  longer  column  for  diffusion. 

5.  Data. — In  table  i  a  few  of  the  data  made  in  1900  are  inserted,  chosen 
at  random. 

In  the  intermediate  time  I  did  not  return  to  the  measurements  until  quite 
recently  (January  1911),  when  a  second  series  of  observations  was  made. 
As  much  as  one-fourth  of  the  air  contained  in  1900  had  now,  however, 
escaped,  in  consequence  of  which  the  above  method  had  to  be  modified  and 
all  heads  measured  in  terms  of  mercury.  Hence  if  H  denotes  the  height 
of  the  barometer  (diminished  by  the  head  equivalent  to  the  vapor  pressure 
of  water)  and  if  m/M  be  neglected  in  comparison  with  i  (about  0.06  per 
cent),  the  equation  becomes 

_  Mgp^  H{l/pm-l/pg)  f    s 

^-      ^  r  ^^ 

in  which  the  first  factor  of  the  right-hand  member  is  constant.  If  the 
observations  are  made  at  the  instant  the  swimmer  sinks  from  the  free 
surface  in  A,  fig.  2,  H  must  be  increased  by  the  mercury  equivalent  of  the 


LIQUIDS  AND  ALUBD  EXPERIMENTS. 


height  h"  of  v.  The  table  contains  all  the  data  reduced  to  mercury  heads. 
A  =  Mgpm/R-  Consequently  1 842  X  io~^  grams  of  the  imprisoned  air  escaped 
in  the  intervening  10.92  years;  i.  c,  0.265  of  the  original  mass  of  air.  In 
other  words  168.7X10"^  grams  per  year,  0.462X10"*  grams  per  day,  or 
5.35  X  io~*^  grams  of  dry  air  per  second. 

Table  i. — Weight  m  of  the  imprisoned  air,  v,  fig.  i.     M=\o  grams;  pm=i3-6; 
Pg=2.^T,  mouth  of  diver,  2r  =  o.2  cm.;  A  =0.0465.    Time  interval  10.92  years. 


Date. 

Barometer. 

Manometer. 

Absolute 
temperature. 

wXio-* 

Feb.  27,  1900 

Feb.  27,  1900 

Jan.  27,  1911 

cm. 

77.21 
77.21 
75-77 

cm. 

—  3.20 

—  2.36 
—21.02 

e 

297.1 
299.2 
296.0 

gms. 
6952 
6950 
5110 

6.  Conditions  of  Flow. — It  is  now  necessary  to  analyze  the  above  experi- 
ment preparatory  to  the  computation  of  constants.  The  mouth  of  the 
swimmer  had  an  area  of  but  0.0314  cm.^.  When  sunk,  the  head  of  water 
above  the  surface  v  was  h"  =  24  cm.  The  column  of  water  between  v  and  d 
was  h'"  =  S  cm.  Hence  the  length  of  column  within  which  transpiration 
took  place  was  24+ 2  X  8  =  40  cm.  The  right  section  of  this  column  is  taken 
as  0.0314  cm.^  throughout.  Naturally  such  an  assumption,  accepted  in  the 
absence  of  a  better  one,  is  somewhat  precarious ;  but  it  may  be  admitted, 
inasmuch  as  the  pressure  of  the  gas  sinks  in  the  same  proportion  in  which 
the  breadth  of  the  channel  enlarges.  Thus  there  must  be  at  least  an  approxi- 
mate compensation.  In  more  definite  experiments  a  cylindrical  swimmer 
whose  internal  area  is  the  same  as  the  annular  area  without  will  obviate 
this  difficulty  (see  fig.  2). 

The  pressure-difference  urging  the  flow  of  air  from  v  is 

Ap  =  24 X0.997  X 98 1  =  23,470  dynes/cm.^ 
hence  per  dyne/cm.^  per  sec. 


-12 


io~"X5.346 


=  10 


'X2.28 


10X2.347 
grams  of  air  escape  from  the  swimmer. 

A  few  comparisons  with  a  case  of  viscous  flow  may  here  be  interesting. 
Using  Poiseuille's  law  in  the  form  given  by  O.  E.  Meyer  and  Schumann's 
data  for  the  viscosity  of  air,it  would  follow  that  but  0.194X  io~^cm.^of  the 
0.0314  cm.^  of  right  section  at  d  is  open  to  intermolecular  transpiration. 
The  assumption  of  capillary  transpiration  is  of  course  unwarrantable  and 
the  comparison  is  made  merely  to  show  that  relatively  enormous  resistances 
are  in  question. 

Again,  the  coefficient  of  viscosity 

V  t     "K     r     .    2       J. 

i-f4f/r"  w  16  IKr    ~^^ 
may  be  determined  directly.     In  this  equation  m  is  the  number  of  grams 
of  air  transpiring  in  t  seconds  through  the  section  irr^  and  in  virtue  of  the 


4  THE   DIFFUSION   OF  GASES  THROUGH 

pressure  gradient  (P-p)/l,  when  rj  is  the  viscosity  and  f  the  slip  of  the  gas. 
Hence  the  value  77/(1  -i-^^/r)  =  4.8  X  lo*^  would  have  to  obtain,  a  resist- 
ance which  would  still  be  enormously  large  relative  to  the  viscosity  of  air 
(17=  180  X  io~^),  even  if  the  part  of  the  section  of  the  channel  which  is  open 
to  capillary  transpiration  is  a  very  small  fraction. 

7.  Coefficients  of  Transpiration. — To  compute  the  constants  under  which 
flow  takes  place  the  concentration  gradient  dc/dl  may  be  replaced  either  by 
a  density  gradient  dp/dl  or  a  pressure  gradient  dp/dl.  If  the  coefficients 
in  question  be  k^  and  kp  respectively 

h  —  ^p  —      ^^ 
"'  Yt  ^  '^dp/dl  ^^^ 

where  the  section  a  is  equal  to  the  area  of  the  mouth  of  the  swimmer,  R  is 
the  absolute  gas  constant,  r  the  absolute  temperature  of  the  gas,  and  m  the 
loss  of  imprisoned  air  in  grams  per  second,  li  v  =  mRr/p  is  the  correspond- 
ing loss  of  volume  at  r  and  p, 

"     Rt      aRrdp/dl  ^^  ^ 

If  in  equation  (3)  the  full  value  of  m  is  inserted,  and  /  denotes  current  time 
or  in  =  m/t;  if 

dl         h"+2h"' 

where  p^  is  the  density  of  water,  h"  and  //'"  the  difference  of  level  (see  fig.  2) 
of  the  surface  in  v  below  the  free  surface  in  A  and  above  the  mouth  at  d, 
the  relations  are 

Mp„Hi-\-2h"'/h' 


k  = 


ii-d 


Rt     T  ap^ 

K  =  k,Rr  (5) 

The  acceleration  of  gravity  g  has  dropped  from  both  equations ;  k^  is  inde- 
pendent of  Rt.     The  coefficient  kp,  however,  is  more  perspicuous. 

If  h'"  is  made  very  small  in  comparison  with  h"  (care  being  taken  to 
avoid  loss  of  air  during  manipulation),  h"  will  also  vanish;  or  for  h"  =  0, 

tRap^  T  \p^      pgj 
and  similarly  for  h"  =  o 

reduces  to 

'm  =  kj,ap^g 

Thus  the  apparatus  is  most  sensitive  if  a  is  as  large  as  possible  and  h'"/h" 
as  small  as  possible  and  the  length  of  the  column  in  A  is  eventually  without 
influence  on  the  result.     Hence  if  for  a  cylindrical  swimmer  the  internal 


UQUIDS  AND  AIvUBD  EXPERIMENTS.  5 

right  section  is  equal  to  the  area  of  the  annular  space  between  the  outer  wall 
of  the  swimmer  and  the  inner  wall  of  the  vessel  A ,  if  the  column  of  water 
above  the  swimmer  is  removed  during  the  prolonged  intervals  of  time 
between  observations,  the  section  a  through  which  capillary  transpiration 
takes  place  is  definitely  given.  It  is  obvious  that  the  swimmer  must  be 
suspended,  for  instance  by  fine  cross-wires,  above  the  bottom  of  the  tank  A . 
Reference  is  finally  to  be  made  to  convection  and  to  temperature.  The 
manipulation  during  observation  necessarily  stirs  up  the  water  and  distorts 
the  regular  pressure  gradient.  Hence  observations  are  to  be  made  rarely. 
Again,  to  obviate  convection  in  general  the  vessel  must  be  kept  in  a  room 
of  nearly  constant  temperature. 

8.  Values  of  the  Coefficients. — If  the  data  of  table  i  be  inserted  in  the 
equations  for  kp  and  k^, 

k  =  J^ll-  =  5-35Xio-"X2.87Xio^X298  ^^         ^^_6 
"     adp/dl  10314X23470/40 

ifep  =  V^T  =  0.29X10-'' 

Hence  for  a  gradient  of  i  dyne  per  centimeter,  2.9X10"*'  grams  of  air 
flow  between  opposed  faces  of  a  cubic  centimeter  of  water  per  second. 
This  may  be  put  roughly  as  about  2.4X10-'"  c.c.  of  air  per  second.  The 
speed  of  migration  of  individual  air  molecules  intermolecularly  through  a 
wall  of  water  is  thus  2.4 X 10"'"  cm. /sec.  for  a  dyne/cm.  gradient. 

Since  the  gradient  is  the  energy  expended  when  the  cubic  centimeter  is 
transferred  i  cm.  along  the  channel,  and  if  the  number  of  air  molecules  per 
cubic  centimeter  be  taken  as  7V  =  60X 10'^,  the  force  acting  per  molecule  to 
give  it  the  velocity  just  specified  is  1/(60X10'*)  dynes.  Hence  the  force 
or  drag  per  molecule,  if  its  speed  is  to  be  i  cm.  per  second,  is 

/~  — 7Z — ^^0 ~r~r, — Ts  — Z', — 8 dynes  /=  6.9X  io-"dynes  if  »=cm./sec. 

^     2.4X10  '°  60X10'*      144X10*   -^         ^        ^  ^  ' 

This  may  be  compared  with  the  force  necessary  to  move  a  small  sphere 
through  a  very  viscous  liquid  of  viscosity  77.     This  force  is 

\iv=\  cm./sec,  2r=  io-*X2  cm.  the  diameter  of  the  sphere  of  influence  of 
the  molecule,  and/=6.9Xio-"  dynes,  the  value  just  found, 

6.9X10-"        _^     _6 

^=6VxTo-*=^''>^^^ 

In  other  words,  the  molecule  moves  through  a  liquid  about  twice  as  viscous 
as  the  air  itself. 

rt  is  not  improbable  that  from  results  of  this  kind  some  light  will  be 
thrown  on  the  molecular  interspaces  of  a  liquid ;  for  the  problem  in  hand  is 
ultimately  that  of  a  single  molecule  transferring  through  the  intermolecular 
channels.     The  relations  here  obtained  will,  however,  be  considerably  modi- 


6  THE  DIFFUSION  OF  GASES. 

fied  in  the  next  chapter  in  connection  with  newer  values  for  N  and  a  more 
trustworthy  value  of  the  diffusion  coefficient  k  than  can  be  obtained  through- 
out the  vicissitudes  of  a  long  time  interval  of  eleven  years  and  a  form  of 
diver  such  as  is  here  used. 

9.  Conclusion. — The  above  data  are  subject  to  the  different  hypotheses 
stated ;  but  it  has  been  shown  that  the  results  may  be  obtained  by  the  method 
described  free  from  ulterior  suggestion.  It  seems  to  me  that  detailed  inves- 
tigations of  the  above  kind  carried  on  with  reference  to  both  the  chemical 
and  the  physical  properties  of  the  liquid,  i.  e.,  with  different  liquids  and 
different  gases  at  different  temperatures  and  pressures,  can  not  but  lead  to 
results  of  importance  bearing  on  the  molecular  physics  involved.  Hence 
experiments  of  this  kind  were  begun  in  this  laboratory  and  such  as  have 
matured  are  reported  in  the  following  chapters. 

Obviously  in  a  doubly  closed  water  manometer  (U-tube),  the  unequal 
heads  of  the  two  columns  of  liquid  must  in  a  way  similar  to  the  above  vanish 
in  the  lapse  of  time.  This  method  seems  particularly  well  adapted  to 
obviate  convection,  and  has  also  been  adopted,  though  it  requires  long 
time  intervals.  Finally,  hydrogen  actually  shows  a  measurable  amount  of 
molecular  transpiration  in  the  daily  march  of  results  obtained;  but  their 
extremely  complicated  character  was  not  foreseen  at  the  outset.  They  are 
not,  therefore,  available  for  discussion  until  they  have  been  thoroughly 
analyzed  in  the  way  to  be  treated  in  Chapter  II. 


CHAPTER  II. 


THE  TRANSPIRATION  OF  THE  SYSTEMS  AIR-AIR,  HYDROGEN-HYDRO- 
GEN, AIR-HYDROGEN,  HYDROGEN-AIR,  ETC.,  THROUGH  WATER. 

10.  Introductory.  Apparatus. — In  the  preceding  chapter  preliminary 
data  were  given  for  the  molecular  transpiration  of  air,  obtained  from  an 
eleven-year  period  of  observations  of  the  increase  of  weight  of  a  Cartesian 
diver.  This  apparatus  was  ill-adapted  for  the  experiments,  because  of  its 
small  mouth.  Consequently  cylindrical  swimmers  have  since  been  in- 
stalled, both  for  air  and  for  hydrogen,  and  often  showed  sufficiently  rapid 
progress  to  admit  of  a  statement  of  results  after  several  weeks.  In  fig.  3, 
vd  is  the  diver  in  the  column  of  water  A,  usually  resting  in  an  elevated 
position  on  the  vertical  wire-gauze  partition,  e.  The  imprisoned  air  is 
shown  at  v  in  contact  with  the  lower  water-level,  and  /  is  the  level  of  the 
free  surface  of  water.      The  . 

tubes  a  and  b,  the  latter  con-         .^f  1 11 0 

taining  a  glass  stopcock,  are 
useful  in  exhaustion,  or  in 
special  experiments  for  the 
conveyance  of  an  artificial 
atmosphere  of  hydrogen  into 
the  space  above  the  free  sur- 
face/. T  is  the  thermometer 
placed  eccentrically.  The 
heads  h',  h",  h'"  will  be  re- 
ferred to  below. 

This  form  of  apparatus 
is  suitably  modified  in  the 
way  shown  in  fig.  4,  with 


Fig.  3. — Cylindrical 
diver  adjusted  for  dif- 
fusion measurement. 


Fig.  4. —  Cartesian   diver 
with  double  tube. 


a  view  to  making  uniform  the  section  of  the  column  of  water  through 
which  diffusion  takes  place.  Here  the  swimmer  vd  is  contained  in  a  central 
tube  cd  (with  a  stopcock  at  c)  full  of  water.  The  swimmer  fits  the  tube 
with  just  sufficient  freedom  to  slide  easily.  The  tube  is  then  partially 
surrounded  by  the  water  in  the  larger  vessel  A .  There  may  be  a  stop  near 
the  top  at  /  to  determine  the  level  of  flotation.  This  is  particularly  neces- 
sary, both  here  and  in  fig.  3,  when  the  top  of  the  swimmer  is  flat.  The 
advantages  of  this  form  are  many;  in  the  first  place,  the  section  r  and  the 
annular  section  r'of  the  diffusion  column  may  be  made  the  same  throughout, 
within,  around,  and  above  the  swimmer,  which  is  not  the  case  in  fig.  3; 
the  level/  may  be  sharply  determined,  since  there  is  no  danger  of  the  rider 
parting  the  water  at  the  surface.  Discrepancies  due  to  friction  of  convec- 
tion currents  are  diminished.    The  heads  h\  h",  and  h'"  may  be  more 

7 


8 


THE  DIFFUSION   OF  GASES  THROUGH 


accurately  measured.  Finally,  the  whole  arrangement  is  more  conducive 
to  constancy  of  temperature  in  the  essential  parts  of  the  apparatus  than  is 
the  case  in  fig.  3. 

1 1 .  Imprisoned  Hydrogen  Diffusing  into  Free  Air.     Preliminary  Data. — 

As  before  the  mass  m'  of  hydrogen  contained  at  v  in  the  swimmer  is  given  by 

R       r   \Pu,       pj  ^  ^ 

where  Mg  is  the  weight  of  the  glass  swimmer,  p^  the  density  of  mercury  at 
0°  C,  p„  the  density  of  water  at  t°,  and  p,  the  density  of  glass.  H  is  the 
barometric  height  diminished  by  the  head  equal  to 
the  vapor  pressure  of  water  vapor,  t  the  absolute 
temperature,  and  R  the  gas  constant  of  hydrogen. 
The  latter  applies  at  the  outset  only.     Since 

3/=  1 8.09  grams  p„=i3,6 

^  =  981  i?  =  4i.4Xio*' 


the  constant  A  =  Mgp„/R  =  0.005823.  The  hydro- 
gen used  was  obtained  electrolytically  from  water, 
enough  being  introduced  into  the  swimmer  to  just 
prevent  flotation. 

In  the  course  of  time  the  gases  contained  in  the 
diver  will  change  from  the  influx  of  diffused  air  and 
the  efflux  of  hydrogen.  Hence  the  gas  constant  R 
of  the  imprisoned  gas  is  not  fixed  in  value.  Sup- 
posing, however,  all  observations  to  be  made  or  all 
diffusion  to  occur  at  a  certain  mean  pressure  B  and 
temperature  t;  since  for  all  gases  i?p  =  i?oPoi  the 
latter  referring  to  the  initially  pure  gas  at  the  given 
temperature  and  pressure  (supposed,  as  stated,  to 
be  constant  during  flotation);  and  since,  finally, 
m  =  v'p  =vp,  during  and  before  flotation,  therefore 

MgPr, 


Fig.  5. — Loss  of  mass 
of  gas  in  diver  in  lapse 
of  days.  Diffusion  of 
hydrogen  into  air. 


v= 


RoPo 


T    ^Pw        Pg^  ^Pw        Pa^  B 


(1') 


so  that  the  variations  of  volume  v  are  referred  to  in  taking  the  quantity 
A  =  Mgp^/R  constant.  To  pass  from  v  to  the  mass  m  it  will  be  necessary  to 
multiply  A  by  p/po  where  the  density  p  of  the  imprisoned  gas  is  not  known. 
I  shall  suppose  that  the  variation  of  temperature  and  pressure  during  a  long 
period  may  be  eliminated  by  the  method  of  least  squares.  Hence  only  the 
coefficients  of  diffusion  by  volume,  called  k  below,  are  determinable.  The 
coefficient  of  diffusion  by  mass,  k,  can  not,  apparently,  be  foimd  at  once, 
except  for  a  system  of  but  one  gas. 

Table  2  contains  the  observations  made  preliminarily  with  hydrogen,  in 
so  far  as  they  are  trustworthy.     These  and  others  are  reproduced  in  fig.  5, 


LIQUIDS  AND  ALLIED  EXPERIMENTS.  9 

tn'  being  shown  in  the  lapse  of  time.  The  curve  is  at  first  nearly  linear  in  its 
descent  and  thereafter  is  sharply  flexed  to  the  right.  This  is  in  a  measure 
due  to  the  fact  that  much  hydrogen  has  escaped,  and  the  lower  surface  of  the 
bubble  V  is  now  no  longer  equal  to  the  area  or  cross-section  of  the  swimmer. 
Hence  the  transpiration  proceeds  with  diminished  area,  and  therefore  more 
slowly.  Subsequent  experiments,  however,  will  show  that  this  flexure  of 
the  curve  is,  in  the  main,  real  (§23). 

There  are  other  difficulties  which  ultimately  enter,  owing  to  the  fact  that 
the  exhaustion  needed  to  make  the  diver  float  is  so  large  that  the  gases 

Table  2. — Molecular  transpiration  of  hydrogen  into  air,  through  a  wall  of  water. 
^=0.005823;  Af=  18.09  grams;  pm=i3.6;  i/p^  =  o.3486*;  A'  =  o.o6  cm.;  A"=ii.o 
cm.;  A"'  =  5.5  cm.;  /  =  22.o  cm.;  areas  12.6  cm.*  and  24.6  cm.*;  c=  12.0  cm.*;  mean  t, 


°;2?=4i.45Xio«;p/,= 

=  89.55X10- 

J 

Date. 

Hour, 
afternoon. 

H 

/ 

wXio« 

-mXio" 

h.      m. 

cm. 

"C. 

gtns. 

gtns./secf 

191 1.  Feb.    8 

0      0 

67.74 

19.4 

883 

6.23 

9 

I     30 

66.29 

21.5 

858 

6.27 

9 

4      0 

65.99 

22.4 

852 

6.37 

10 

4      0 

62.44 

23.2 

804 

Mean: 

II 

0      0 

58.27 

22.4 

752 

6.29 

12 

5     20 

5305 

23.4 

683 

»3 

4      0 

49.41 

22.8 

637 

14 

3     30 

45-44 

21.9 

587 

»5 

5      0 

40.93 

19.8 

532 

*Provisional  value.    See  §  24. 

fTaken  from  four-day  groups:  Feb.  9  to  13;  10  to  14;  11  to  15. 


dissolved  in  the  water  come  out,  on  exhaustion,  prior  to  observation. 
Hence  all  these  results  are  discarded.  To  obtain  a  long  period  of  trust- 
worthy values  the  diver  should  either  be  weighted  (a  heavier  diver  will 
hereafter  be  used)  requiring  more  gas  to  float  it,  or  the  gas  should  be  in 
excess,  so  that  the  diver  sinks  only  under  excess  of  pressure.  Both  modi- 
fications are  in  a  measure  undesirable.  Massive  parts  endanger  the  accu- 
racy of  the  temperature  datum,  and  pressure  excess  requires  a  U-tube  man- 
ometer, which  is  less  easily  read  at  an  instant  than  the  barometric  form. 
Hence 

^,=  1.07X10-"  k^  =  k^RT=i.3iXio-'  (§12) 

=  1.15X10-''  k^  =  kj,RT  =1.40X10-'  (§13) 

Observations  of  the  above  kind,  though  exceptionally  delicate  in  them- 
selves, are  marred  by  a  difficulty  which  I  have  not  quite  been  able  to  over- 
come. Whenever  the  temperature  differs  from  that  of  the  room  there  will 
be  vortical  convection  currents,  which  by  their  friction  on  the  walls  of  the 
diver  tend  either  to  raise  or  to  depress  it.  Hence  such  experiments  should 
preferably  be  made  in  a  room  of  constant  temperature  (if  available),  or  at 
least  in  the  summer. 


lO  THE   DIFFUSION   OF   GASES  THROUGH 

12.    Continued.     Coefficients  Depending  upon  Water  Heads  Only. — It 

will  be  expedient  to  compute  the  coefficients  of  molecular  transpiration, 
tentatively,  under  a  variety  of  hypotheses,  before  making  a  more  careful 
examination  of  the  case.  There  are  at  the  outset  two  points  of  view  from 
which  the  coefficients  of  transpiration  may  be  calculated,  since  in  fig.  3  the 
gas  at  V  (hydrogen),  is  different  from  the  gas  at/  (air).  Thus  the  pressure 
gradient  may  either  be  taken  as  the  mere  excess  of  pressure  at  v  over  that 
off,  i.e., 

dp  _     h"p^g     _         p^g 

dl       h"^2h"'       \-\-2h"'lh"  ^^' 

since  hoth  gases  hydrogen  and  air  are  saturated  with  moisture ;  or  the  gradient 
may  be  taken  as  the  full  barometric  pressure  plus  the  head,  i.e., 

dp  _  H-\-h"p^g 


dl  h"-\-2h 


in 


(3) 


since  there  is  no  hydrogen  above  /  and  both  gases,  hydrogen  and  air,  are 
saturated  with  water.  To  decide  between  these  and  other  hypotheses  it 
will  ultimately  be  necessary  to  introduce  for  comparison  an  artificial  atmos- 
phere of  hydrogen  at/,  as  is  done  in  §20  below.  Moreover,  if  the  diffusion 
takes  place  subject  to  equation  (3),  air  must  in  like  manner  diffuse  from/ 
into  V,  and  a  phenomenon  of  considerable  complication  result,  as  is  actually 
the  case. 

Leaving  the  theoretical  discussion  for  more  adequate  treatment  below,  it 
is  interesting  preliminarily  to  examine  equations  (2)  and  (3)  separately. 
Postulating  equation  (2),  the  (virtual)  coefficients  k  for  a  pressure  gradient 
are  respectively,  if  a  is  the  area  of  the  mouth  of  the  swimmer,  and  m'  the 
loss  of  imprisoned  air  per  second  for  the  gradient  dp/dl, 

m'  m'  i+2h"'/h" 

k  =  — ; — tt;  = (4) 

adp/dl       a  p^g 

Here  2h"'  =11  cm.,  h"=ii  cm.,  therefore  i-\-2h"' /h"  =  2.  The  mean  tem- 
perature may  be  taken  at  22°  or  p„ =0.998;  ^  =  981,  a=i2  cm.^  thus 

2 

^  =  in' — — o^  o    =  i7oXio~^w' 

12X0.998X981 

The  pressure  gradient  dp/dl  is  489  dynes/cm.     Hence,  since 

m=  —  6.29X1  o~^°g/sec. 

the  value  of  the  initial  coefficients  is  at  22°,  for  hydrogen,  if  the  air  influx 
is  ignored, 

j^  =  1.07X10"" 

Here  k  is  the  rate  in  grams/sec,  under  the  hypothesis  stated,  at  which 
hydrogen  transpires  molecularly  between  opposed  faces  of  a  cubic  centi- 
meter of  water,  when  the  gradient  is  one  dyne/cm. 


UQUIDS  AND  ALLIED   EXPERIMENTS.  II 

I  may  remark  in  passing  that  from  equation  (4) 

m'  =  kap^g/{i^2h"'/h") 

the  individual  values  of  m'  from  day  to  day  should  vary  with  p„  or  with 
temperature;  but  this  amounts  to  but  0.02  per  cent  per  degree  and  is  thus 
insufficient  to  explain  the  zigzag  passage  of  some  of  the  curves  obtained; 
for  instance,  that  of  the  transpiration  of  air  into  air  through  water  (§19), 
or  of  hydrogen  into  hydrogen  (§20) ,  quantitatively.  Moreover,  the  zigzag  is 
of  a  positive  and  negative  character  and  hence  quite  beyond  the  reach  of 
such  a  discrepancy.  It  has  been  referred  partly  to  the  effect  of  vortices 
due  to  convection  (frictional  pull  of  water  on  the  swimmer),  or  again  to  an 
actual  evolution  and  absorption  of  the  imprisoned  gas  from  the  water  below, 
as  temperature  rises  and  falls.  Finally,  since  the  true  mass  rate,  w,  for 
mixed  gases  is  obtained  from  m',  by 

m  =  m  —  (5) 

Po 

where  Po  refers  to  hydrogen  and  therefore  for  the  given  mixture,  c(Bt.  par., 
m  is  constant,  m'p  must  also  be  constant.  In  other  words,  m'  as  computed 
will  vary  inversely  as  the  actual  density  p  of  the  gas,  i.  e.,  m'  will  increase 
as  temperature  rises  and  decrease  as  temperature  falls.  The  effect  of 
temperature  is  not,  however,  marked  in  these  experiments.  It  is  so,  how- 
ever, for  an  air-air  system,  for  which  the  latter  explanation  does  not  apply, 
Hence  the  cause  of  the  irregularity  is  probably  absorption  and  release,  as 
specified. 

13.  Continued.  Apparent  Frictional  Resistance  per  Molecule.  Virtual 
Viscosity. — The  above  coefficient,  k,  nominally  shows  the  grams  per  second 
of  hydrogen  which  transpire  molecularly  for  a  pressure  gradient  of  one 
dyne/cm.  at  22°.  As  the  density  of  hydrogen  at  22°  is  about  82.3X10"' 
the  volume  coefficient  will  be 

K  =  V82.3Xio~®=  1.30X10"' 

Here  k  is  the  true  coefficient  of  transpiration  by  volume. 

It  may  be  interesting  to  inquire  in  passing  what  the  virtual  viscosity  would 
be  under  which  the  molecule  transpires  for  a  pressure  gradient  of  dyne/cm. 
when  1.3X10"^  c.c.  of  hydrogen  transpire  molecularly  between  opposed 
faces  of  a  cubic  centimeter,  or  the  velocity  of  the  molecule  is  2)=  1.3  X 10"' 
cm. /sec.  If  the  resistance,  which  is  really  kinetic,  be  regarded  as  due  to  a 
continuous  medium  of  virtual  viscosity  ri,  we  may  write  the  force  /  urging  a 
single  molecule  of  radius  r  with  a  speed  v 

f=6irr]rv 

Thus  the  force  which  urges  iV  =  6oX  10^^  molecules  (O.  E.  Meyers's  estimate 
of  the  number  per  cubic  centimeter,  if  the  efifective  diameter  of  each  is 
2r  =  2  X  io~^  cm.)  will  be 

F  =  3T77X2Xio~'X6oXio'^X» 


12  TBCe   DIIflfUSION  OP  GASES  THROUGH 

Now,  the  above  velocity  corresponds  to  a  pressure  gradient  dyne/cm.,  i.  e., 
to  a  loss  of  energy  of  i  erg  per  cubic  centimeter  for  a  transfer  of  the  cubic 
centimeter  of  gas  along  i  cm.,  /".  e.,  to  a  resistance  of  F=  i  dyne.  Thus  for 
the  stated  value  of  v 

77  =  68Xio~^ 

The  viscosity  of  hydrogen  at  22°,  according  to  Puluj,  is  91.5  X  io~\  Hence 
if  the  present  method  of  computation,  which  ignores  the  air  influx,  were  cor- 
rect, it  would  follow  that  the  molecular  transpiration  of  hydrogen  through 
the  intermolecular  pores  of  water  takes  place  at  a  rate  corresponding  to  the 
order  of  its  viscosity.  The  experiments  of  the  sequel  (§§19,  20),  however, 
show  that  this  simple  method  of  computation  is  not  admissible  for  hydrogen- 
air  dififusion,  or  at  least  not  until  the  pressure  gradients  due  to  the  heads  of 
water  quite  hold  in  check  the  further  influx  of  air  due  to  diffusion. 

14.  Continued.    Transpiration  Depending  upon  Barometric  Pressure. — 

If,  again,  the  initial  influx  of  air  into  the  swimmer  be  ignored,  while  the 
eflflux  of  gas  due  to  diffusion  gradients  is  alone  considered,  the  gradients 
take  the  form 

dp        (B-T)p„-i-h''p^ 

where  B  is  the  height  of  the  barometer  and  p„  and  p„  the  densities  of  mercury 
and  water,  r  the  vapor  pressure  of  water  vapor  (referred  to  mercury),  h" 
the  effective  head  of  water,  h"-\-2h"'  the  length  of  the  diffusion  column. 
The  mean  temperature  was  22°,  the  mean  barometer  76.21  cm.,  and  the 
vapor  pressure  2  cm.    Thus 

#_    o    74-21 X 136+ 1 1X0.998  ,        , 

—  =  981  ^ ^^[^i =45.500  dyne/cm. 

whence,  since  a=  12  cm.^  and  ^'  =  6.29X10"^°,  the  auxiUary 

k  =  m'/a{dp/dl)=^  I. iSXio'^^ 

If  these  coefficients  be  taken  per  cubic  centimeter  instead  of  per  gram  of 
hydrogen  transpiring  per  second,  under  normal  conditions,  the  volume 
coefficient  will  be 

K  =  V82.3Xio~^=  1.40X10"" 

Hence  the  velocity  of  transpiration  for  a  dyne/cm.  gradient  is  z)=  1.4X  io~" 
cm./sec. 

Finally  the  virtual  viscosity  of  the  medium  through  which  the  single 
molecule  is  dragged  by  the  gradient  would  be,  since  the  resistance  F=  i, 

77  =  i/GirNrv  =  6,3 10  X  io~® 

In  other  words,  the  viscosity  under  the  tentative  hypothesis  stated  would  be 
about  70  times  as  large  as  that  of  hydrogen. 


LIQUIDS  AND  ALLIED   EXPERIMENTS.  1 3 

The  decision  as  to  the  applicability  of  either  of  these,  or  similar  hypoth- 
eses, can  not  be  given  until  the  work  is  repeated  with  an  artificial  atmos- 
phere of  hydrogen  at/ in  fig.  3,  in  place  of  air;  or  after  other  similar  varia- 
tions of  experiment.  The  results  (§20)  show  that  in  the  earlier  stages  of 
the  work,  at  least,  the  behavior  throughout  is  then  totally  different.  Hence 
it  is  necessary  to  investigate  the  question  from  a  broader  point  of  view  and 
relative  to  the  two  simultaneous  diffusions  in  opposite  directions  through 
the  same  channel. 

15.  Continued.  Influx  of  Air  into  the  Imprisoned  Hydrogen. — In  view 
of  the  fact  that  for  a  single  gas  m  increases  uniformly  in  the  lapse  of  time, 
the  initial  counterflux  of  air  may  also  be  computed  directly,  independent 
of  the  flow  of  hydrogen.  In  this  way  additional  light  is  thrown  upon  the 
phenomenon,  preliminarily.     Thus  if  k^  and  p^  refer  to  air 

U,        h   n^H    'Al-h   ^(^-'^)PmS-pa_t.  ^^  74-21  X 13-6X981  ,. 

ma=KadpJdl=kaa — f^ft^^h'"  "     22 ^^^ 

where  p^  is  zero  at  the  beginning  of  the  experiment  and  where  k^  has  the 
value  found  in  §19,  i.ogXio~^^.  Hence  Wa  =  5.89X10"^  grams/sec.  or 
5.09 X I o~' grams/day.  Initially  (/  =  o  sec),  therefore,  the  swimmer  should 
gain  5.1  mg.  per  day,  due  to  the  influx  of  air  into  the  imprisoned  hydrogen. 
In  the  lapse  of  time  this  rate  would  naturally  be  much  reduced  in  conse- 
quence of  the  counter-pressure  of  the  air  accumulating  in  the  swimmer; 
nevertheless  the  initial  rate  of  influx  (5.89X10"*  grams/sec.)  is  so  large,  as 
compared  with  the  observed  rate  of  efflux,  6.29  X  io~^°  grams/sec.  in  table  2, 
as  to  show  that  two  counter-currents  of  air  and  hydrogen  are  simultaneously 
transpiring,  at  rates  relatively  not  very  different  in  value.  It  is  therefore 
necessary  to  investigate  these  currents  in  detail. 

16.  Continued.  Coeffidents  Depending  on  Diffusion  Gradients.  TranS' 
piration. — This  case  might  at  first  seem  improbable.  If  the  hydrogen 
diffuses  outward  under  full  barometric  pressure  at  v,  fig.  3,  there  being  no 
hydrogen  at  /,  the  air  must  diffuse  inward  from  /  to  v,  since  there  is  no 
air  originally  at  v;  but  when  the  hydrogen  has  nearly  vanished,  or  its 
pressure  excess  at  v  is  equivalent  to  a  diffusion  gradient  h"ptog  along  fv, 
the  air  or  a  mixed  air-hydrogen  gas  would  again  have  to  diffuse  outward, 
due  to  the  specified  head  or  increment  of  pressure  at  v  as  compared  with  /. 
Such  complications  would  hardly  be  expected  in  so  simple  an  experiment 
and  yet  this  is  precisely  what  seems  to  take  place.  I  have  therefore  developed 
the  equations  tentatively  as  follows. 

Let  p,^  and  />„  be  the  pressures  of  hydrogen  and  of  air  at  any  time  at  v, 
fig.  3.  Let  B  be  the  constant  barometric  pressure  during  diffusion  and  tt 
the  vapor  pressure  of  water.    Then 

B-\-h"p„g  =  p,+p,+T  (8) 

where  the  constant  ll  =  pn-\-pa  =  B+h"p„g—Tr  may  be  used  for  abbreviation. 


14  THE  DIFFUSION   OF  GASES  THROUGH 

Let  nta  and  m,^  be  the  masses  of  air  and  of  hydrogen  transpiring  per  second, 
into  and  out  of  the  imprisoned  volume,  v.  Hence,  if  a  is  the  area  of  the 
water  level  at  v, 

-m=-  {m^  -  w  J  =  a{k^  dpjdl  -  k^  dpjdl)  (9) 

is  the  variation  of  mass  per  second,  if  kj^  and  k^  are  the  coefficients  for  hydro- 
gen and  air,  respectively.     But 

dp^  ^  B-TT-Pa  ^  pH-h"p^g  dpj,  ^        pj, 

dl  h"+2h"'  h"+2h"'  dl  h"+2h"'  ^^^^ 

where  p„  is  the  density  of  water  and  g  the  acceleration  of  gravity.     Hence 

Therefore,  when  p^  vanishes  in  the  lapse  of  time,  the  diffusion  of  air  alone 
is  in  question  and  m  will  be  constant.  The  datum  actually  measured, 
however,  is  m'  =  mp/pg,  where  p  is  the  density  of  the  imprisoned  mixed  gas 
and  Pg  the  density  of  the  initial  gas,  hydrogen,  all  at  the  supposedly  fixed 
mean  temperature  and  pressure  assumed.  Thus  it  will  be  necessary'-  to 
refer  equation  (11)  to  diffusion  by  volume  and  write,  k  being  the  coefficient, 

-t,  =  fl(K,-0  ^n^^^n,  +^'af^n_^^f^,„  (12) 

In  equation  (12)  if  p^  were  to  vanish  or  become  negligible,  the  transpira- 
tion of  air  would  alone  be  in  question  and  v  would  be  constant,  supposing 
that  Kf^  and  k^  are  really  constant,  or  that  the  phenomenon  is  homogeneous. 
For  a  diffusion  and  a  transpiration  phenomenon  may  occur  side  by  side, 
subject  to  different  laws ;  the  first  depending  upon  the  degree  of  mixture  of 
the  gases  and  rapidly  vanishing  as  the  mixture  is  more  nearly  complete, 
the  second  depending  upon  the  head  h".  It  does  not  follow,  however,  in 
view  of  §15,  that  Pj,  will  vanish  first;  for  when  pn  =  h"p^g,  Pa  =  B  —  Tr,  and 
the  influx  of  air  must  cease,  because  the  air  gradient  has  vanished.  Hence 
thereafter  hydrogen  and  air  will  both  diffuse  out  of  the  swimmer;  for  any 
further  diminution  of  p,,  means  an  increase  of  />„  which  is  now  greater  than 
B  —  TT.  A  mixture  of  gases  thus  diffuses  which  grows  continually  richer  in 
air  and  poorer  in  hydrogen,  until  it  is  nearly  pure  air. 

Equations  (11)  and  (12)  are  not  integrable,  since  wis  independent  of  wand 
V  independent  of  v. 

17.  Continued.  Flotation. — Admitting  equation  (12),  the  endeavor 
must  now  be  made  to  express  P}^  or  its  equivalent  in  terms  of  quantities 
belonging  to  the  mixture,  or  to  express  m  in  terms  of  p,  the  density  of  the 
imprisoned  gases. 

Let  P  be  the  artificial  barometric  pressure  on  flotation,  and  let  p^  and 
pJ^  be  the  corresponding  pressiures  of  the  dry  air  and  hydrogen  imprisoned. 


LIQUIDS  AND   ALLIED  EXPERIMENTS.  1 5 

Then  if  the  position  of  the  swimmer  remains  unaltered  and  temperature  is 
constant 

P+h"p,g-ir=p',+p^=^n'  (13) 

while  above,  equation  (8) 

B-\-h"p^g-ir  =  p^-^p^  =  n 
n'  is  variable  in  time,  whereas  n  is  constant.     Moreover 

B-P={pa-p'a)  +  {pH-p[)^^P==PaVPn  (h) 

Pa+'ph  =  ^  (15) 

The  ratio  (Pa-\- Ph) / (Pa~'r  Ph)  is  not  the  same  as  B/P  but  equal  to  U/u'. 

The  imprisoned  volume  v'  at  constant  temperature  on  flotation  will  be 
rigorously 

,^  M{i/p^-i/p„) 

i-PJR^Pt-PJR^Pt-t/R,p,t  ^'^^ 

if  jR  is  the  gas  constant  for  air,  hydrogen,  and  water  vapor,  as  indicated 
by  subscripts.  The  second,  third,  and  fourth  terms  of  the  denominator  are 
not  larger  than  0.00098  at  ordinary  temperatures  and  variable  to  less  than 
o.ooooi  per  degree.  Hence  they  are  negligible  as  compared  with  the  large 
variations  of  m  found  in  experiment,  which  amount  to  several  per  cent. 
Thus 

v'  =  Mii/p^-i/p„)  (17) 

nearly  enough  for  all  purposes,  and  hence 

in  terms  of  mercury  heads  if 

A=v'p„g,  (19) 

the  condition  of  flotation  is 


m- 


We  may,  on  the  other  hand,  express  the  pressures  without  coefficients, 
v'  being  given  by  equation  (17), 

»'n'=(i?„m,+J?,w,)r  (21) 

Again,  since  ©'  is  constant, 

v'P=iR^ma+Rnm)r  (22) 

at  constant  temperature;  or  from  equation  (18) 

A 


(z+l!)  (-) 


1 6  THE  DIFFUSION  OF  GASES  THROUGH 

Between  the  variables  belonging  to  11  and  11'  respectively  there  is  an  imme- 
diate relation,  since  on  mere  expansion  for  flotation 

PjPn  =  p'jPn  (24) 

at  any  time,  from  which  p'  may  be  reduced  to  p;  or,  for  instance,  in  case 
of  equation  (18) 


m 


^'  (Pa    ,Ph\Ph..^  (      X 


Finally,  the  initial  mass,  m^,  of  hydrogen  imprisoned  must  be  given, 
corresponding  to  the  initial  volimie  t'  =  fo,  not  expanded  like  v'  for  flotation; 
V  is  variable  while  v'  is  constant.     Hence 

m^  =  v^^lRj^r  (26) 

and  at  any  subsequent  time 

m=m,+w,=  ^(|5  +  |^)  (27) 


which  reduces  to 


-7(i-i)+4"  (-> 


p  being  the  density  of  the  mixture  undergoing  transpiration  at  /  seconds 
and  po  the  density  of  the  pure  hydrogen  at  /  =  o  seconds. 

The  value  of  p^  given  in  equation  (29)  may  now  be  inserted  into  equation 
(11),  whereupon  this  becomes 

which  is  perhaps  the  most  acceptable  form  of  the  equation  for  m;  but,  as 
stated  above,  it  can  not  be  integrated,  because  p  =  Pa-\-pj^  =  m/v,  both  of 
which  (m  and  v)  are  variable  in  the  lapse  of  time.  Since  m'  =  mpjp  is 
observed,  the  equation  is  advantageously  referred  to  volume.  If  the  mean 
temperatture  and  pressure  are  assumed  constant  throughout,  implying 

R,pIR^P^  =  RJR 

where  R  the  gas  constant  of  the  mixture, 

'v  i-RjR     K^-K,  h"p„g 

a  ~  ^  I  -  RjRn  h"+2h"'  ^  "  h"-\-2h'"  ^^^^ 

If  w  or  i)  is  constant,  a  result  which  eventually  appears  in  all  the  experi- 
ments, it  follows  that  p  is  constant,  i.  e.,  a  gas  mixture  of  definite  composi- 
tion or  density  eventually  diffuses,  since 

'^-''^^h"+2h"'  R,-R,p, 


LIQUIDS  AND  AI^LIED  EXPERIMENTS.  1 7 

but  the  density,  p,  of  this  mixture  is  not  given.     If,  however,  m  is  observed 
p  may  be  computed  (equation  31).     If  p  =  po 

-m  =  aUkJ{h"+2h"')-aUJl-h"pg)/{h"-\-2h'")  (33) 

depending  upon  two  nearly  equal  counter-currents,  since  II  is  relatively 
large.     If  eventually  p  =  Pa,  since  R^ p^  =  RnpQ  =  Rn Pn, 

-m  =  ak^h"p„g  (34) 

the  diffusion  of  air  alone  due  to  the  head  h". 

Finally,  in  a  manner  similar  to  the  above,  one  may  deduce 

ra 


v  = 


U{h"  +  2h"') 


77rApn{RaK-\-RM-RaKh"p„g]  (35) 


18.  Continued.     Potential  Energy  of  the  gas  mixture. — If  the  mixed 
gases  are  to  be  separated,  the  work  to  be  done  is  given  by 

W  =  vp^Xog  pJn+vp,\og  pjli  (36) 

since  the  hydrogen  is  to  be  compressed  isothermally  from  v  and  Pf^  to  11 
and  the  air  similarly  from  v  and  p^  to  11,  v  being  the  volume  of  gas  while 
transpiration  is  taking  place  at  n  =  />j+/>a-  Thus  the  work  per  unit  of 
volume  is 

'^»=V  =  ^""'^n^.+"'°«^"=><'^^^T^       (37) 

If  there  is  eventually  to  be  but  a  single  gas  present,  the  above  equation  for 
W  must  be  modified,  to  include  the  relative  importance  of  the  head  h"  of 
water  on  the  imprisoned  gas.     In  other  words, 

Pn+Pa  =  ^+h"p„g^Tl+p'  (say) 
and  therefore 

^=P^o,:^^+in+p')Xo,'^±^^  (38) 

Hence,  if  p^^  is  equal  to  zero,  on  expansion  (since  P'/Ti.  is  also  very  small) 

-={^+P')  (^  +  •  •  •)=/''  =  A"p«^,  nearly. 

The  potential  energy  per  unit  of  volume  is  constant. 

The  rate  at  which  potential  energy  is  lost  per  second  on  mixture  is  per 
unit  of  volume 

-  =  -Pnlog[-j^  -  ij  +  -log^^^^i ^^ (39) 

if   »=o,  dW/dp.=  -vlog^'^^  ~^* 

Ph 
iipn  =  o,  dW/dv=W/v 

lfPn=Tl-^p'  or  pa  =  o,  initially, 

iv       •  ^     Ph       '  ,^ 

—  = -/>logo+/>;^ -log— =  -/> log o+/>'-,  nearly. 


1 8  THE   DIFFUSION  OF   GASES  THROUGH 

It  follows  therefore,  initially,  when  />^  =  !!+/>'  or  />a  =  o,  there  being  a 
charge  of  hydrogen  only, 

W  lv=  00 
for  all  reasonable  values  of  p^  and  v.  Hence  diffusion,  to  keep  pace  with  the 
loss  of  potential  energy  per  second,  should  be  extremely  rapid  at  the  outset. 
The  observations  below,  as  a  rule,  show  enormously  rapid  transpiration 
at  the  beginning  of  the  experiment,  which  thereafter  rapidly  diminishes  and 
is  often  reversed  in  the  lapse  of  time.  There  can  be  little  doubt,  therefore, 
that  in  the  cases  of  mixed  gases  the  rate  at  which  the  potential  energy  of 
the  system  diminishes  may  be  invoked  to  interpret  the  observed  phenom- 
enon, particularly  when  the  diffusion  take  place,  on  the  whole,  against  the 
gradients  due  to  the  water  heads.  Beyond  this,  however,  i.  e.,  further  than 
as  a  means  of  pointing  out  the  source  of  energy,  the  potential  energy  of 
separated  gases  will  not  probably  need  to  be  considered. 

19.  Transpiration  of  Air  into  Air  Through  Water. — Tentative  results  of 
this  kind  were  given  in  the  preceding  chapter,  from  observations  lasting  a 
period  of  about  eleven  years.  The  swimmer  was  unsuitable  for  the  purpose, 
but  the  datum  found,  k  =  2.gXio~^^,  should  furnish  an  estimate  as  to  the 
probable  order  of  values  to  be  anticipated. 

In  table  3  I  have  given  the  present  results,  so  far  as  they  have  matured, 
showing  the  daily  diminution  of  the  mass  (m  in  grams)  of  the  imprisoned  air. 

Figure  6  contains  the  value  of  m  in  milligrams  on  successive  days.  As 
the  observations  can  not  be  in  error,  even  as  much  as  o.i  per  cent,  the 
marked  discrepancy  encountered  must  have  some  real  cause.  True,  the 
opportunities  for  constant  temperature  were  not  at  hand  and  there  is  inter- 
ference with  the  gradient  due  to  convection,  in  the  case  of  an  apparatus 
like  fig.  3 ;  but  the  actual  increase  of  weight  can  not  apparently  be  referred  to 
these  causes,  except  in  so  far  as  w  =  w'p/po ,  in  equation  (5).  There  are  two 
other  explanations :  If  the  temperature  of  the  column  of  water  is  not  exactly 
that  of  the  environment  during  observation  there  will  be  eddy  currents, 
which  will  raise  and  depress  the  swimmer  by  friction  with  its  sides.  This 
was  actually  tested  on  February  27  by  artificially  heating  the  apparatus 
from  without.  The  swimmer  is  then  too  heavy,  due  to  a  downward  axial 
current  and  the  charge  of  air  found  too  small.  The  discrepancy,  however, 
is  inadequate  in  amount.  The  predominating  cause  seems  to  be  associated 
with  the  effect  of  temperature  on  the  solution*  of  gases  in  water.  At  higher 
temperatures  gas  is  evolved  from  the  water  and  caught  by  the  swimmer 
and  the  imprisoned  air  is  therefore  too  heavy.  At  lower  temperatures  the 
gas  of  the  swimmer  is  absorbed  into  water  and  the  charge  of  air  is  too  light. 
As  this  effect  is  inherent  in  the  experiment  itself,  there  is  no  way  of  com- 
bating it  except  the  maintainance  of  absolutely  constant  temperature. 
The  coefficients  will  eventually  have  to  be  computed  by  the  method  of 

*The  final  curve  for  the  hydrogen-hydrogen  system  is  much  smoother  than  the 
corresponding  curves  for  mixed  gases  under  the  same  conditions.  Hence  the  pref- 
erence given  to  the  solution  effect. 


LIQUIDS  AND  ALLIED  EXPERIMENTS. 


19 


Table  3. — Diffusion  of  air  through  water  into  air. 


Mgp^H/  I 


R 


( );M=  12.01  grams;i?  =  2.87Xio'';p;„=i3.6;.4=lfgpm/2?  =  o.05583; 

/  =  28.ocm.;A"=  15.0cm.;  2/»"'=  13.0cm.:  i/P(,  =  o.3486;*  water  heado.ii  cm. 
Diameters:  Vessel  =  4.3  cm.;  float  =  2.5  cm.       Areas:  A'=i4.^  cm.*;  ^1=7.05  cm.* 


Date. 

j    Hour. 

1 

Barometer. 

H 

/ 

Observed 
wXio" 

Computed 
rnXio* 

AmXio* 

1    . 

!   A.     m.    i 

0 

Jan.  31.. 

75.89 

69.51 

17.8 

8548 

8498 

+  50 

Feb.    I.. 

76. 

73       i 

69.50  1 

18.4 

8523 

8463 

+  60 

2.  . 

t     *  * 

75 

10 

67.71 

19.4 

8259 

8428 

-169 

3-- 

76 

80      1 

65  54 

16.4 

8262 

8393 

-131 

4.. 

. .  . 

74 

76 

66.69 

22.2 

8255 

8358 

-103 

6.. 

77 

04 

64- 57 

15.2 

8172 

8288 

-116 

I-- 

76 

16 

64.22 

16.6 

8091 

8253 

-162 

8.. 

76 

44 

64 -33 

18.7 

8051 

8218 

-167 

9.. 

75 

84 

65  34 

22.4 

8075 

8183 

-108 

10.  . 

75 

49 

66.21 

23.1 

8174 

8148 

+  26 

II.. 

76 

54 

65.22 

22.8 

8058 

8114 

-  56 

17.. 

4 

00 

76 

>5 

61.16 

17.0 

7697 

7904 

—207 

18.. 

4 

«5 

75 

37 

64.72 

26.2 

7916 

7869 

+  47 

19.. 

4     35 

76 

06 

64.59 

24.0 

7952 

7834 

+  118 

20.  . 

4    45 

75 

01 

63  57 

21.3 

7892 

7799 

+  93 

21 . 

4    45 

75 

88 

62.98 

21.5 

7813 

7764 

+  49 

22. 

4     35 

75 

30 

62.67 

22.2 

7758 

7729 

+  29 

23- 

4     40 

75 

51 

62.54 

22.0 

7747 

7694 

+  53 

24.. 

4     »5 

74 

87 

62.91 

24.2 

7741 

7659 

+  82 

25- 

'     3     15 

75 

52 

63.46 

26.8 

7747 

7624 

+  123 

26. 

4     10 

75 

72 

63.58 

25.6 

7790 

7590 

+200 

27- 

4     00 

75 

91 

62.98 

23.8 

7758 

7555 

+203 

28. 

!     4     05 

76 

14 

61 .  15 

20.6 

7607 

7520 

+  87 

Mar.    1 . 

3     50 

75 

00 

61.28 

23.6 

7553 

7485 

+  68 

2. 

3     40 

74 

7' 

62.26 

27.0 

7598 

7450 

+  148 

3- 

3     35 

75 

64 

58.89 

15.6 

7444 

74«5 

+  29 

4- 

3     40 

75 

99 

59-35 

21 . 1 

7372 

7380 

-     8 

5- 

5     00 

77 

04 

58.95 

21 .0 

7325 

7345 

—  20 

6. 

4    00 

76 

37 

5^  '1 

23.2 

7297 

7310 

-    13 

7- 

3     30 

77 

25 

58.76 

22.2 

7273 

7275 

—     2 

8. 

3     45 

76 

60 

59.12 

24.8 

7261 

7240 

+  21 

9- 

3     45 

76 

02 

58.91 

22.0 

7297 

7205 

+  92 

10. 

3     45 

74 

59 

57.78 

18.3 

7240 

7170 

+  70 

1 1  . 

3     45 

76 

38 

56.93 

18.5 

7130 

7135 

-     5 

12. 

4    00 

75 

87 

56.01 

16.6 

7056 

7100 

-  44 

13- 

4     00 

76 

73 

56. 10 

18.9 

7016 

7066 

-   50 

14. 

3    45 

76 

59 

55-09 

17.0 

6932 

7031 

-  99 

«5- 

3    45 

74 

44 

55-55 

20.0 

6923 

6996 

-  73 

16. 

4    00 

75 

44 

53  94 

13.1 

6874 

6961 

-  87 

•7- 

3     30 

76 

64 

53-51 

16.6 

6742 

6926 

-184 

18. 

3     45 

75 

80 

54-92 

22.4 

6794 

6891 

-  97 

19. 

4    00 

76 

04 

55.87 

22.9 

6900 

6856 

+  44 

20. 

3     30 

74 

•5" 

56.30 

23.2 

6964 

6821 

+  143 

21 . 

3    45 

75 

•57 

55  31 

20.2 

6889 

6786 

+  103 

22. 

3     30 

74 

.61 

54.80 

20.7 

6815 

6751 

+  64 

23- 

3     30 

75 

.46 

54  34 

18.8 

6799 

6716 

+  83 

24. 

3     30 

76 

•54 

53.20 

'7-5 

6684 

668 1 

+     3 

25- 

3     45 

77 

.02 

52.34 

17.2 

6582 

6646 

-  64 

26. 

•      4    30 

76 

•54 

52.80 

21.4 

6552 

6611 

-   59 

27. 

•      3     45 

75 

.07 

53  25 

21.5 

6606 

6577 

+  29 

28. 

•      3     45 

74 

•59 

53-97 

22.3 

6678 

6542 

+  136 

29. 

4     00 

74 

.83 

53-64 

22.2 

6640 

6507 

+  133 

30. 

4     00 

73 

•77 

53-27 

21 .2 

6614 

6472 

+  142 

31- 

4     00 

74  58 

52.55 

19.6 

6573 

6437 

+  136 

*Cf.  §24. 


20 


THH   DIFFUSION  OF  GASES   THROUGH 


Table  3 — Continued. 


Date. 

Hour. 

Barometer. 

H. 

/. 

Observed 
wXio'. 

Computed 
mXio*. 

A  wXio^ 

A.  w. 

Apr.     I 

•     3    30 

75-37 

51.40 

17.6 

6455 

6402 

+  53 

2 

5    00 

75-97 

49.92 

15.9 

6304 

6367 

-  63 

3 

•      3     30 

76.71 

49.18 

16.3 

6202 

6332 

-130 

4 

.      4    00 

77.07 

48.68 

16.3 

6139 

6297 

-.58 

5 

4    00 

75-27 

48.80 

17.2 

6137 

6262 

-125 

6 

•      3    45 

75-31 

49.64 

19.5 

6197 

6227 

-  30 

7 

.      3     00 

75-47 

50.08 

20.2 

6238 

6192 

+  46 

8 

•      4    30 

76-43 

49-39 

18.0 

6195 

6157 

+  38 

9 

•     4    30 

76.28 

48.49 

17.0 

6101 

6122 

—  21 

10 

.     4    00 

76.86 

48.34 

19.0 

6045 

6087 

-  42 

II 

.     3     30 

77-25 

47-98 

19.0 

6000 

6053 

-  53 

12 

•     3    30 

77-52 

47-58 

18.2 

5964 

6oi8 

-  54 

>3 

4    00 

77.36 

47.27 

18.8 

5914 

5983 

-  69 

14 

•      3    45 

76.26 

47.07 

«7-5 

59«3 

5948 

-  35 

least  squares.  The  run  of  the  thermometer  on  the  same  sheet,  fig.  6,  bears 
out  this  surmise.  The  barometer,  like  the  vapor  pressures,  shows  no  easily 
discernible  relation  to  the  weight  curve;  but  the  run  of  temperature  fore- 
shadows the  kinks  in  the  m  curve  throughout  its  extent. 


(Te^.    5      10      15      ZO      ^cMatZ      7      1Z     117     32      ZZ  dpri       6 

Fig.  6. — Loss  of  mass  of  gas  in  diver  in  lapse  of  days.     Diffusion  of  air  into  air. 

If  we  write  for  the  air-water  system  (time  /  in  days,  mass  m  in  grams) 

and  compute  the  constants  Wq  and  m  by  the  method  of  least  squares  from 
the  68  observations  made  between  January  31  and  April  11,  the  values 
obtained  are 

Wq  =  0.008532 7  gram  m = 0.00003493  gram/day 


LIQUIDS  AND  ALLIED  EXPERIMENTS.  21 

The  data  for  m  calculated  with  these  constants  are  also  inscribed  in  table  3. 
The  errors  show  the  fluctuation  of  the  temperature  cycles.  They  may  be 
regarded  as  eliminated  from  the  curve  as  a  whole.  The  rate  m  per  day 
reduced  to  seconds  gives 

w  =  4.04X10"^°  grams/sec,  at  about  20° 
Hence 

4.04X10"*°  _13 

k=  ^^ =1.09X10 

7.05X524 

The  new  value  is  thus  much  smaller  than  the  tentative  value,  k  =  2.9X  io~*' 
found  from  the  balloon-shaped  Cartesian  diver,  with  small  mouth  (2f  =  0.2 
cm.)  after  a  period  of  eleven  years.  The  uncertainty  surrounding  the  latter 
datum,  in  view  of  the  long  time-interval  and  the  unfavorable  shape,  etc.,  did 
not  lead  me  to  expect  more  than  an  order  of  values.  The  values  of  k, 
moreover,  involve  the  change  of  the  gas  constant,  or  mixtiu-e.  Nevertheless 
the  agreement  should  apparently  have  been  closer.  Moreover,  even  in  the 
present  method,  a,  h",  and  h'"  are  not  yet  very  accurately  determinable 
and  the  equation  l  =  h"-\-2h"'  needs  a  correction  for  2h"'.  The  path  out  of 
and  around  the  diver  is  actually  longer  than  2h"'.  It  does  not,  however, 
seem  worth  while  to  apply  these  refinements  until  a  room  of  perfectly  con- 
stant temperature  has  been  secured. 

Finally,  it  is  interesting  to  compute  the  virtual  viscosity  of  the  inter- 
molecular  space  through  which  the  air  molecule  transpires.  The  coefficient 
of  diffusion  taken  per  cubic  centimeter  (k  being  independent  of  R  and  there- 
fore correct)  mil  be 

1.09X10""  ^     _io 

K=  — =0.91X10  ^" 

0.0012 

whence  the  velocity  of  transpiration  for  a  gradient  of  dyne/cm.  is  also 
»  =  9. 1 X  io"*°  cm./sec.     Writing,  as  above, 

H  =  F/6irNrv 
where  F  =  i  dyne,  iV  =  60  X 10**  molecules  per  cubic  centimeter,  2r = 2  X  io~' 
cm.  (O.  E.  Meyer's  values), 

_  I _5 

''"  6X3-i42X6oXio*«Xio"«Xo.9iXio"*''~^7''>^''' 
The  viscosity  of  air  is  190  X  io~®.    Thus  the  virtual  viscosity  of  the  medium 
is  to  this  extent  about  5  times  that  of  normal  air. 
If  we  take  Millikan's*  recent  data  for  N  and  2r,  viz, 

iV  =  2.64Xio"     2f  =  2.89X10"*  (oxygen)      2r= 3.06X10"*  (nitrogen) 

and  regard  2f  =  3Xio"*  cm.  as  the  average  molecular  diameter  for  air, 
2Nr= 0.7932  X 10**  replaces  2Nr  =12X10"  above ;  whence 

7J=  1455X10"* 

or  the  virtual  viscosity  of  the  intermolecular  medium  would  be  nearly  8 
times  as  large  as  normal  air. 

*Millikan,  Physical  Review,  xxxn,  pp.  349  et  seq.,  igii. 


22  THB  DIFFUSION  OF  GASKS  THROUGH 

If  the  correction  for  Stokes's  law  be  introduced,  v  must  be  replaced  by 

i+2^/r 


:;  = 


i+3fA 


where  ^  is  the  coefficient  of  slip.     If  ^  =  7.6X  io~^  an  order  of  values  given 

by  Millikan  (/.  c),  since  2r  is  but  3  X  io~^,  v  is  to  be  replaced  by  2v/s.    This 

makes  rj  about  50  per  cent  larger,  or  the  virtual  viscosity  of  the  medium  is 

finally 

17  =  2180X10"® 

or  about  11. 5  times  as  large  as  the  viscosity  of  normal  air.  Finally,  if  the 
correction  for  the  density  of  glass  given  in  §24  is  inserted,  this  factor  is 
increased  to  about  13. 

20.   Transpiration   of    Hydrogen   into   Hydrogen   Through   Water. — 

The  behavior  of  hydrogen  alone  is  peculiar.  Hydrogen  was  imprisoned  in 
the  swimmer,  as  usual,  on  the  first  day  (see  table  4).  The  upper  surface 
was  still  in  contact  with  atmospheric  air;  hence  the  marked  loss  of  weight, 
the  potential  energy  of  separated  gases  being  dissipated  at  the  initial  very 
large  rate.  Thereafter,  however,  the  air  was  replaced  by  an  artificial 
atmosphere  of  hydrogen  from  the  gasometer,  whereupon  the  large  loss  of 
weight  from  February  25  to  26  almost  at  once  changes  to  a  gain,  which  in 
its  turn  at  first  grows  enormously,  finally  to  decrease  again  to  a  smaller  but 
still  persistent  gain.  This  feature  is  probably  due  to  the  air  dissolved  in 
the  water  (see  fig.  7).  Temperature  modifies  these  data  somewhat,  but 
the  fact  remains  that  hydrogen  apparently  diffuses  through  water,  from 
low  to  high  pressure;  i.  e.,  up-hill  or  against  the  pressure  gradient.  This 
is  an  interesting  result,  showing,  like  the  first  sudden  drop,  the  importance 
of  the  mixture  effect.  The  potential  energy  of  separated  gases  is  being 
dissipated  at  a  rapid  rate.  Possibly  some  dissolved  air  at  first  diff'uses  into 
the  swimmer;  but  eventually  hydrogen  diffuses  into  it  in  excess  of  the 
outgo  of  air;  for  in  view  of  the  pressure  />„  of  the  diffused  air  within  the 
swimmer  and  since  pj,-'rpa  is  constant,  p,,  is  less  than  the  pressure  B—xoi 
the  artificial  atmosphere  of  hydrogen  on  top.  The  data  after  March  2  and 
as  far  as  March  9  show  the  trend  of  approximately 

w=i.7  =  io~®g/day  or  o.2Xio~^°g/sec. 

the  result  being  a  remarkably  regularly  increase  of  weight.  One  may  note 
that  all  these  changes  of  direction  are  abrupt.  Whether  this  is  merely  acci- 
dental or  whether  certain  definite  mixtures  diffuse  together  remains  to  be 
seen.  Unfortunately  air  is  not  a  simple  gas,  so  that  the  behavior  of  three 
gases  is  really  involved. 

A  pecuhar  result  during  this  stage  of  diffusion  and  occtu-ring  in  all  similar 
cases  is  the  enormous  enlargement  of  microscopic  air  bubbles  attached  to 
the  solid  surfaces  wherever  they  are  in  contact  with  water.  These  are 
sought  out  by  the  hydrogen,  and  soon  become  visible  and  greatly  enlarged 


LIQUIDS  AND  ALLIED  BXPERIMENTS. 


23 


by  the  flow  of  hydrogen  into  them,  so  that  they  finally  break  off  or  may  be 
shaken  off.  After  the  first  few  days  such  bubbles  no  longer  occur.  This  is 
additional  confirmation  to  the  effect  that  hydrogen  here  diffuses  from 
apparent  low  pressure  to  apparent  high  pressure,  so  far  as  water  levels  are 
concerned,  in  cases  where  it  enters  a  medium  of  air, however  small;  i.  g.,the 
gradients  due  to  mixture  imply  that  pa^ft''PuS>  /'h^-S  — tt,  since  pa-\-Ph  = 
B-\-h"pj„g  —  ir  is  constant.  Wherever  the  water  is  continuous  or  in  actual 
contact  with  the  glass,  no  bubbles  are  produced.  Neither  do  they  ever 
occur  for  the  diffusions  of  air  into  air. 

Table  4. — Diffusion  of  hydrogen  through  water  into  hydrogen. 

A  =0.005823;  Jl/=  18.09;  Pm=i3-6;  A' =  0.8  cm.;  /*"=  ii.ocm.;  h"'  =  S-5  cm.; /= 22.0 cm.; 

I /Pj,  =  0.3486*;  water-head  0.06  cm.  Hg. 

Areas:  12.6  cm.';  24.6  cm.'.     Diameters:  4.0  cm.;  5.6  cm. 


Date. 

Hour. 

Barometer. 

H 

t 

Observed 

TWXlO* 

Computed 
wXio« 

AwXl0« 

h.    m. 

0 

Mar.  15 

4    00 

74-44 

61 .51 

20.0 

799 

804 

-   5 

16 

4    00 

75 

44 

59.67 

13. 1 

793 

795 

—    2 

17 

3     30 

76 

64 

59.19 

16.9 

777 

785 

-  8 

18 

4    00 

75 

80 

60.18 

22.6 

776 

775 

+   1 

•9 

4    00 

76 

04 

59.65 

22.4 

769 

765 

+  4 

20 

•      3     30 

74 

51 

59.46 

23.4 

764 

756 

+  8 

21 

•      3     45 

75 

57 

58.03 

20.2 

754 

746 

+  8 

22 

3     30 

74 

61 

56.97 

20.9 

739 

736 

+  3 

23 

•      3     30 

75 

46 

55.66 

19.0 

726 

726 

0 

24 

•      3     30 

76 

54 

54.01 

17.8 

707 

717 

—  10 

25 

•      3     45 

77 

02 

53'7 

17.7 

696 

707 

—  II 

26 

•      4     30 

76 

54 

5325 

21.5 

689 

697 

-  8 

27 

•      3     45 

75 

07 

53.16 

21.8 

687 

688 

—   I 

28 

•      3     45 

74 

59 

53.02 

22.4 

684 

678 

+  6 

29 

4    00 

74 

83 

52.37 

22.2 

676 

668 

+  8 

30 

4    00 

73 

77 

51.63 

21 .2 

668 

658 

+  10 

31 

4    00 

74 

58 

50.53 

19.6 

657 

649 

+  8 

Apr.     I 

3     30 

75 

37 

48.99 

17.9 

641 

639 

+  2 

2 

5     00 

75 

97 

47.4« 

16.0 

624 

629 

-  5 

3 

•     3     30 

76 

71 

46.51 

16.6 

613 

619 

-  6 

4 

4    00 

77 

07 

46.01 

16.5 

605 

610 

-  5 

5 

4    00 

75 

25 

45.49 

16.8 

597 

600 

-  3 

6 

•      3     45 

75 

31 

45.82 

19.7 

596 

590 

+  6 

7 

3     00 

75 

47 

45.39 

20.2 

589 

580 

+  9 

8 

•      4     30 

76 

43 

44-'7 

18.2 

577 

57« 

+  6 

9 

•      4     30 

76 

28 

43.02 

•7-3 

564 

56. 

+  3 

10 

4    00 

76 

86 

42.46 

19.2 

553 

551 

4-  2 

II 

•     3     30 

77 

25 

41.36 

19.0 

539 

542 

-  3 

12 

3     30 

77 

52 

40.05 

17.8 

524 

532 

-  8 

'3 

4    00 

77 

36 

39.62 

19.1 

516 

522 

-  6 

•4 

•     3     45 

76.25 

38.98 

17.8 

510 

512 

—  2 

*Cf.  §24. 


After  March  9,  however,  the  regular  decrease  of  weight  begins,  again 
abruptly,  due  to  the  transpiration  of  hydrogen  in  accordance  with  the 
pressure  gradient  (water-heads)  alone.  After  March  20  it  progresses  with 
satisfactory  uniformity  until  April  14,  when  the  experiments  w^ere  broken 
off,  as  it  seemed  improbable  that  further  characteristic  changes  would  occur. 


24  THE  DIFFUSION   OF  GASES  THROUGH 

To  compute  the  constants  for  the  diffusion  of  hydrogen  into  hydrogen 
through  water,  data  from  March  17  to  April  14  were  treated  by  the  method 
of  least  squares,  as  shown  in  table  4.     If 

f»  =  Wq  —  mt 
(time  in  days)  the  constants  are 

Wo  =  814.1X10"®  grams  w  =  9,734X10"®  grams/day 

From  these  the  rate  per  second  follows  as 

m=  i.i266Xio~*°g/sec. 
The  constants  of  the  apparatus  are 

a=i2cm.'^  /f"=iicm.  2h"'=ii  cm.  /  =  22cm. 

Thus 


li  ~  ¥+^'  "  489  dyne/cm. 


and  therefore 


m  -M 


involving,  however,  the  change  of  gas  constant.  Hence  the  true  coeflBcient 
K,  referred  to  unit  of  volume  transpiring,  if  the  density  of  hydrogen  be 
taken  as  89.5  X  io~®  is 

K  =  2.i4Xio~^° 

or  the  velocity  of  transpiration  is  2.14 X  io~^°  cm. /sec.  This  is,  therefore, 
more  than  twice  as  large  as  in  case  of  air,  where  k  =  o.9i  X  io~^°. 

If  follows,  finally,  that  the  virtual  viscosity,  77,  of  the  intermolecular  gas 
through  which  the  hydrogen  molecule  supposedly  transpires,  if  iV=6oX  10", 
2r  =  2Xio~*cm.  (O.  E.  Meyer),  is 

r]=  i/67riVr'i)  =  o.ooo4i3 

The  viscosity  of  hydrogen  at  ordinary  temperatures  is  normally  91.5  X  io~*. 
Hence  the  virtual  viscosity  of  the  intermolecular  hydrogen  would  be  four 
and  a  half  times  larger  than  its  normal  viscosity. 
Using  Millikan's  data  for  N  and  r,  viz, 

iV  =  2.64X10^®  2f  =  2.28Xio~''cm. 

the  datum  2iVr  =  6.03Xio"  replaces  2AV=  12,0X10",  whence 

77  =  826X10"® 

Here  in  turn  the  discrepancy  of  Stokes's  equation  is  to  be  added.  If  it 
is  applied,  the  value  of  17  will  be  further  increased  about  50  per  cent  or  the 
virtual  viscosity  of  the  intermolecular  medium  is  finally 

77  =  1240X10"® 


LIQUIDS  AND  ALUED  EXPERIMENTS. 


25 


or  about  13.5  times  the  normal  viscosity  of  hydrogen.  Correcting  as  in  §24, 
the  factor  becomes  15,  which  does  not  agree  with  the  corresponding  datum 
for  air  (about  13  times)  as  well  as  the  values  found  above  appeared  to 
predict. 


^ebA^:kaid 


5?5^r 


Fig.  7. — Chart  showing  loss  of  mass  of  gas  in  diver  in  lapse  of  days. 
Diffusion  of  hydrogen  into  hydrogen. 

21.  Transpiration  of  Imprisoned  Air  into  Hydrogen  Through  Water. — 

The  immediate  use  of  equation  (i)  is  inadmissible,  since  the  gas  constant  R 
varies,  as  the  gas  within  the  swimmer  changes  its  composition.  But  since 
at  a  given  pressure  and  temperature  Rp  is  constant  for  all  mixttues, 


m 


R  T     \pu  Pg/ 


is  still  the  correct  value,  relatively  to  volume,  as  intimated  above.  It  is 
merely  necessary,  therefore,  to  coordinate  the  correct  value  of  p  for  the 
initial  gas  and  its  gas  constant  R,  after  which  the  equation  is  applicable  to 
all  subsequent  gas  mixtures,  if  the  diffusion  k  by  volume  is  to  be  computed; 
but  m  is  now  merely  an  apparent  rate,  and  k  merely  a  transitional  value. 


26 


THE   DIFFUSION   OF  GASES  THROUGH 


The  experiment  of  this  section  is  the  converse  of  those  briefly  detailed  in 

table  2  and  repeated  at  greater  length  in  a  following  paragraph  (23).     The 

data  are  given  in  table  5  and  are  shown  graphically  in  lig.  8.     During  the 

Table  5. — Diffusion  of  air  through  water  into  hydrogen.  M=  14.45;  g  =  98i ;  pm=  '3-6; 
i?a=2. 87X10^;  a  =  6.4cm.-;  A==Mgpm/Ra  =  o.o6~i-j;  h'=i.^cm.;  //"=iocm.;  h"'  =  ^ 
cm.;  I /p(,= 0.3486.* 


Date.     Hour.  ^ 

1 
Barom- 
eter. 

H 

1 

/ 

wxio" 

Date. 

Hour. 

Barom- 
eter. 

H 

/ 

wxio" 

h. 

w. 

0 

h. 

WI. 

0 

Mar.   6 

5 

00 

76.37 

53-59 

21 .4 

8002 

Apr.  12 

3 

30 

77-52 

61.18 

17.8 

9239 

7 

4 

00 

77  25 

57-21 

22.6 

8510 

•3 

4 

00 

77  36 

60.79 

19.3 

9137 

8 

4 

00 

76.60 

61.98 

24.8 

9"  59 

>4 

3 

45 

76.26 

60. 12 

18.0 

9074 

9 

4 

00 

76.02 

64.81 

22.8 

9636 

15 

3 

00 

75.8. 

59-85 

20. 1 

8972 

10 

4 

15 

74-59 

65.70 

18.8 

9890 

16 

3 

30 

75-25 

58.87 

19.2 

8851 

II 

4 

00 

76.38 

66.84 

19.0 

10055 

17 

3 

30 

75-45 

57.10 

18.0 

8618 

12 

4 

00 

75-87 

67.23 

17.1 

10176 

18 

4 

00 

75-67 

55-74 

18.6 

8396 

13 

4 

00 

76.73 

68.36 

19.2 

10277 

19 

4 

00 

75.69 

54.62 

17.0 

8271 

>4 

4 

•5 

76.59 

68.36 

•7-4 

10336 

20 

3 

45 

75.10 

53-52 

16.3 

8I2I 

«5 

4 

00 

74-44 

69.79 

20.4 

I0453 

21 

4 

00 

75   50 

52.52 

16.8 

7957 

16 

4 

00 

75-44 

68.26 

13.1 

10467 

22 

4 

00 

76.14 

51 .  10 

17.0 

7737 

17 

3 

30 

76.64 

68.73 

17. 1 

10402 

23 

4 

00 

76-37 

49-52 

16.2 

75'7 

18 

4 

15 

75.80 

70.03 

22.8 

10410 

24 

4 

00 

76.02 

49-13 

17-5 

7426 

19 

4 

00 

76.04 

69.96 

22.4 

10413 

25 

4 

00 

76.26 

48.19 

18.6 

7259 

20 

3 

30 

74-5" 

70-55 

23.6 

10462 

26 

3 

30 

76.82 

47.16 

18.4 

7108 

21 

3 

45 

75-57 

70.07 

20.5 

1049 1 

27 

3 

•5 

76.88 

46.47 

20.0 

6970 

22 

3 

30 

74.61 

70.13 

21  .0 

10483 

28 

3 

15 

76-33 

46. 16 

21 .0 

6902 

23 

3 

30 

75  46 

69.43 

19.1 

10442 

29 

4 

00 

75-77 

45-43 

21.2 

6788 

24 

3 

30 

76.54 

68.54 

18.0 

10343 

30 

4 

00 

75-58 

44.12 

20.0 

6617 

25 

3 

45 

77.02 

68.40 

17.8 

10328 

May    I 

3 

45 

75.02 

43-66 

20.5 

6537 

26 

4 

30 

76.54 

69.49 

21.8 

10361 

2 

4 

00 

74.91 

43-34 

20.2 

6496 

27 

3 

45 

75-07 

69-74 

21  .9 

10397 

3 

4 

00 

75-7» 

42-77 

19.2 

6430 

28 

3 

45 

74-59 

70.08 

22.6 

10424 

4 

4 

•5 

76.14 

42.48 

19.2 

6387 

29 

4 

00 

74-83 

69.87 

22.5 

10397 

5 

4 

00 

76.35 

42. 12 

18.3 

6351 

30 

4 

00 

73-77 

69.60 

21.5 

10388 

6 

4 

00 

76.48 

41.88 

19.0 

6301 

3' 

4 

00 

74-58 

68.87 

20.0 

10328 

7 

4 

30 

76.06 

4>-54 

19.2 

6246 

Apr.     1 

3 

30 

75-37 

67.76 

20.0 

10226 

8 

4 

00 

75-93 

39.58 

20.5 

5926 

2 

5 

00 

75-97 

66.59 

16.1 

lOIII 

9 

4 

00 

74-95 

38.02 

21.3 

5679 

3 

3 

30 

76.71 

66.08 

17.0 

10003 

10 

4 

00 

75-32 

37-77 

21.5 

5638 

4 

4 

00 

77.07 

65.63 

16.8 

9897 

1 1 

4 

00 

75.69 

37.89 

22.0 

5648 

5 

4 

00 

75-27 

65-35 

17.2 

9889 

12 

4 

00 

75.90 

38.09 

21.8 

5680 

6 

3 

45 

75-31 

65.83 

20.0 

9871 

'3 

4 

30 

75-92 

37-97 

22.3 

5654 

7 

3 

00 

75-47 

65.76 

20.2 

9855 

14 

4 

30 

76.81 

37-56 

20.6 

5623 

8 

4 

30 

76.43 

64.70 

18.3 

9754 

•5 

4 

00 

76.14 

37-29 

20.5 

5583 

9 

4 

30 

76.28 

63-53 

•7-5 

9603 

16 

►  4 

00 

75-74 

37.11 

22.2 

5528 

ic 
II 

4 
3 

00 
30 

76.86 
77-25 

63.21 
62.32 

19.6 
195 

9491 
9360 

>7 

4 

00 

75-93 

37-27 

22.2 

5552 

*Cf.  §24. 

first  days  and  later  the  swimmer  rapidly  increases  in  weight,  at  least  at  first; 
the  influx  of  hydrogen  or  the  initial  apparent  rate  is  about 

w  =0.000550  g/day  =  64  X  lo'^^g/sec. 
and  it  thus  much  exceeds  the  converse  case  of  table  2 ;  but  this  rapid  influx 
is  soon  reduced  in  the  lapse  of  time. 

The  bubble  phenomenon,  due  to  the  diffusion  of  hydrogen  into  micro- 
scopic air-bubbles  adhering  to  solid  parts,  under  water,  was  equally  promi- 
nent. During  the  early  days  these  gathered  in  great  quantity  and  had  to 
be  shaken  off.     It  would  be  interesting  to  estimate  the  virtual  pressure  at 


LIQUIDS  AND  ALLIED  EXPERIMENTS. 


27 


which  the  bubbles  are  initially  expanded.  In  fact,  if  the  pressure  within 
be  taken  as  p  =  ^T/r,  where  T  is  the  surface  tension  and  r  the  radius  of  the 
sphere,  if  the  bubbles  grow  almost  from  the  order  of  microscopic  dimensions, 
say  from  r=io~*  cm.,  we  may  put 

/>  =  4X8o/io~^  =  3.2Xio^  dynes/cm.^ 

Thus  the  initial  pressure  would  have  to  be  of  the  order  of  several  atmos- 
pheres, if  this  explanation  is  correct.  As  not  more  than  one  atmosphere 
is  available,  the  original  air-bubbles  should  be  larger  than  6Xio~^  cm.  in 
diameter  to  expand. 


fskax.  5 


Fig.  8. — Chart  showing  loss  of  mass  of  gas  in  diver  in  lapse  of  days. 
Diffusion  of  air  into  hydrogen. 

Between  March  9  and  16  the  rate  has  somewhat  abruptly  decreased 
(a  to  h  in  curve). 

Between  March  16  and  30  the  weight  of  the  imprisoned  air  was  nearly 
stationary  {b  to  c  in  curve),  a  condition  of  things  which  has  again  been 
reached  abruptly.  Hence  the  per  second  influx  of  hydrogen  and  the  efflux 
of  air  are  here  about  equal,  remembering,  however,  that  m  is  not  the  actual 
mass. 

From  March  20  the  pronounced  efflux  suddenly  begins,  at  a  specific 
though  slowly  increasing  rate  until  April  30  {cde  in  curve).  It  would  seem 
to  be  probable  that  during  this  interval  the  content  of  the  swimmer  is 
largely  hydrogen ;  and  yet  the  apparent  mass  rate  of  efflux  is 

w=i6oXio~' g/day  or  i8Xio~^°  g/sec. 


a  relatively  large  value. 


28  THE  DIFFUSION  OF  GASES  THROUGH 

Since  the  area  of  diffusion  is  a  =  6.4  cm.^  and 

^"  =  10  cm.  h"'  =  5  cm.  /  =  h"  +  2h"'  =  20  cm.  ^  =  490  ^^ 

dl  cm. 

(apparent)  ^  =  o.6Xio~^^.     Thus  the  volume  coefficient  is 

K  =  4.9X10-'° 
Hence  comparing  the  coefficients  per  unit  of  volume  it  appears  that  for 
air-air    k  =  o.9iXio-'*';    for  hydrogen-hydrogen,  k  =  2. 14X10-'°;  for  air- 
hydrogen,  K  =  4.92  X  io-'°. 

Thus  the  present  coefficient  is  over  5  times  as  large  as  the  corresponding 
coefficient  for  air  and  over  twice  as  large  as  the  coefficient  for  hydrogen. 
Hence  the  mixture  transpiring  can  not  be  pure  hydrogen.  The  reason  for 
this  large  k  is  difficult  to  ascertain. 

In  fact  (curve  e  to/)  after  April  30  till  May  7  the  rate  abruptly  diminishes 
again  to 

—  w  =  5 1 X  iQ-^/day  =  5.9  X  io-'°g/sec. 

whence  ^=1.57X10"'°  which  is  now  below  the  value  for  hydrogen,  as  it 
should  be. 

On  May  7,  the  upper  atmosphere  of  hydrogen  was  accidentally  forgotten 
and  replaced  by  air  for  but  one  day.  The  loss  of  weight  thereafter  is 
enormous,  showing  that  the  contents  must  at  least  have  approached  pure 
hydrogen.  The  artificial  atmosphere  of  hydrogen  was  replaced  on  the 
next  day,  but  the  recovery  of  the  curve  is  slow  (/  to  g  in  curve)  and  corre- 
sponds to  the  initial  behavior  of  hydrogen  (§20)  above.  Thereafter  to  June  i  o, 
the  mean  rate  is  —  w  =  26  X  iQ-^  g/day  =  3.0X  io-'°g/sec.  From  this  coeffi- 
cients are  obtained  as  ^  =  0.97  X  iQ-'^  and  k  =  0,8 1 X 10"'°.  Hence,  as  usual, 
the  influx  of  air  has  enormously  reduced  the  final  rate  by  diminishing  the 
partial  pressure  of  hydrogen. 

22.  Transpiration  of  Oxygen  into  Hydrogen  Through  Water. — These 
results,  which  contain  the  first  example  of  the  behavior  of  two  simple  gases, 
are  given  in  table  6  and  in  fig.  9.  One  may  note  the  enormously  rapid  rate 
of  efflux  (a  to  h  in  curve),  on  the  first  day.  The  mean  apparent  rate  (rela- 
tive to  mass)  during  this  day  was  in  fact 

—  w  =  8.2  X  iQ-*  g/day  =  9.5  X  lo"'  g/sec. 

nearly  30  times  as  large  as  the  final  rate  and  about  ten  times  as  large  as  the 
initial  rate  of  the  hydrogen-air  system.  This  might  seem  to  be  due  to  the 
solubility  of  oxygen  in  water,  but  it  will  probably  be  explained  in  terms  of 
the  relatively  high  density  of  this  gas.  The  rapid  diffusion  ceases  after  the 
first  day,  when  the  greater  part  of  the  oxygen  will  have  escaped.  The  case 
is  particularly  remarkable,  as  the  rate  is  necessarily  the  difference  between 
the  influx  of  hydrogen  and  the  efflux  of  oxygen,  so  that  the  actual  rate  of 
loss  of  oxygen  must  have  been  relatively  enormous. 

On  the  six  succeeding  days  (curve,  from  h  to  c)  the  influx  of  hydrogen  into 
the  swimmer  about  balances  the  efflux  of  oxygen  from  the  swimmer.     There- 


LIQUIDS  AND  ALUED  EXPERIMENTS. 


29 


after  (curve,  c  to  d)  the  steady  efflux  begins,  the  behavior  being  at  first  very- 
irregular,  as  usual  for  oxygen.     The  rate  here,  so  far  as  observed,  is 

— f»  =  32  X  io~®  g/day  or  3.7  X 10"  ^°  g/sec. 

The  constants  of  flotation,  etc.,  are 

/i"=i4.5cm.  2//"  =13.6  cm.  /  =  28.1  cm.,  0  =  7.05  cm.' 

Hence 


dp  _ 

—  =  505  dynes/cm.  ^  =  1.04X10  " 

dl 


K  =  0.78X10 


-10 


which  is  somewhat  less  than  the  rate  found  above  for  air  into  air  with  the 
same  apparatus.     What  is  diffusing,  however,  must  be  a  mixture  of  oxygen 

Table  6. — Diffusion  of  oxygen  through  water  into  hydrogen  and  vice  versa.  M=  12.01 
grains;  i?,=2.6oXio*;  p»,=  13.6;  A  =0.0617;  h'=\.\  cm.;  h"—  14.5cm.;  A'"  =  6.8 cm.; 
i//»j=o.3486;*/=28. 1  cm.;areas  14.5cm.*;  0  =  7.05  cm.*,  a'  =  7.45  cm.*;  correction  = 
0.08  cm.  Hg. 


Date,  j  Hour. 

Barom- 
eter. 

H 

/ 

OTXIO* 

Date. 

! 

Hour. 

Barom-      j-t 
eter.       "" 

/ 

wxio" 

h. 

r». 

0 

i 

h. 

m. 

0 

Apr.  14 

5 

00 

76.26 

72.17 

18.2 

9999 

!  May  12 

4 

00 

75.90 

58.03 

21.7 

7953 

"5|  3 

00 

75.81 

66.69 

20.3 

9179 

•3 

4 

30 

75-92 

58 

'7 

22.2 

7960 

16  3 

30 

75-25 

65.89 

19.0 

9107 

«4 

4 

30 

76.81 

57 

75 

20.6 

7942 

•7  3 

30 

75.45  j 65.66 

17.6 

9115 

1            >5 

4 

00 

76.14 

57 

25 

20.5 

7893 

18  4 

00 

75.67    65.64 

18.5 

9086 

i            "6 

4 

00 

75-74 

57 

47 

22. 1 

7867 

'9;  4 

00 

75.69    65.57 

16.8 

9124 

!        17  4 

00 

75-93 

57 

65 

22.1 

7892 

20  3 

45 

75.10    65.65 

16.2 

9<54 

•8!  4 

00 

75-32 

57 

53 

21.3 

7894 

21 

4 

00 

75  50 

65.68 

16.5 

9150 

19 

4 

00 

75.86 

57 

5' 

21 .9 

7878 

22 

4 

00 

76.14 

65.30 

16.8 

9088 

1       20 

4 

00 

76.08 

57 

37 

22.8 

7836 

23 

4 

00 

76.37 

64-55 

16.0 

9007 

21 

4 

30 

76.09 

57 

00 

22.0 

7805 

24 

4 

00 

76.02 

64-49 

17.2 

8964 

22 

4 

00 

75.82 

56 

95 

22.5 

7786 

25 

4 

00 

76.26 

64.91 

18.4 

8987 

1       23 

4 

00 

76.40 

57 

08 

23.2 

7787 

26 

3 

30 

76.82 

64.80 

18.2 

8978 

1       24 

4 

00 

76. 11 

56 

99 

22.8 

7784 

27 

3 

'5 

76.88 

64.92 

20.0 

8945 

25 

4 

00 

75.69 

57 

13 

23.6 

777' 

28 

3 

•5 

76 -33 

65.35   21.0 

8976 

i       26 

4 

00 

75-96 

56 

67 

23-3 

77JO 

29 

4 

00 

75-77 

65.22  21.2 

8952 

1       27 

4 

00 

76.22     56 

00 

22.7 

7651 

30 

4 

00 

75.58 

64.44  20.2 

8873 

i       28 

4 

30 

76.20 

55 

36 

21.6 

7589 

May  I 

3 

45 

75.02 

64.34 

20.6 

8847 

29 

4 

00 

75-95 

55 

37 

21.8 

7586 

2 

4 

00 

74-9" 

64.  II 

20.4 

8821 

30 

4 

00 

76.22 

55 

37 

21.3 

7598 

3 

4 

00 

75.-71 

63.61 

19.1 

8789 

31 

3 

30 

75-91 

55 

39 

21.8 

7589 

4 

4 

15 

76.14 

63 -34 

19.0 

8754 

June    I 

4 

00 

74.96 

56 

07 

23-5 

7643 

5 

4 

00 

76.35 

62.86 

18. 1 

8712 

2 

5 

00 

75-55 

55 

91 

23.4 

7641 

6 

4 

00 

76.48 

62.77 

18.8 

8680 

3 

3 

15 

76.25 

55 

42 

22.1 

7586 

7 

4 

30 

76.06 

62.63 

19.0 

8656 

4 

4 

30 

76.38 

54 

87 

21.6 

7521 

8 

4 

00 

75.93 

60. 12 

20.2 

8278 

!             5 

3 

45 

76.20 

54 

27 

20.2 

7472 

9 

4 

00 

74-95 

57.76 

21 .2 

7926 

1            6 

3 

30 

76.09 

54 

28 

22.0 

7433 

10 

4 

00 

7532 

57.41 

21.5 

7873 

!            8 

1 

4 

00 

76. 1 1 

54 

15 

22.5 

7403 

II 

4 

00 

75.69 

57.69 

21 .9 

7901 

9 

4 

00 

75.70 

54.06 

22.4 

7393 

*Cf.  §24. 

and  hydrogen  with  a  preponderance  of  the  latter,  since  the  inward  diffusion 
of  hydrogen  ceases  when  (subscripts  indicating  the  gases) 

Thereafter,  since  p^  must  decrease  indefinitely,  p,^  becomes  greater  than 
B—ir.    Thus  h"p„g  becomes  an  index  for  the  composition  of  the  diffusing 


30 


THE   DIFFUSION   OF   GASES  THROUGH 


gas  mixture,  here  hydrogen  and  oxygen,  and  it  is  therefore  not  remarkable 
that  the  final  coefficients  of  the  linear  march  are  all  specific  of  the  mixture. 
This  fact  is  particularly  borne  out  by  the  following  phenomenon.  On 
May  7  to  8  the  artificial  atmosphere  of  hydrogen  was  accidentally  replaced 
by  an  atmosphere  of  air  but  for  one  day.  The  usual  effect  of  an  enormous 
loss,  continuing  for  a  day  thereafter,  even  though  the  atmosphere  of  hydro- 
gen was  replaced,  is  apparent  {d  to  e  in  curve).  After  May  9  the  period  of 
recovery  begins,  efflux  and  influx  being  at  first  about  equal  (e  to /in  curve). 
The  rapid  loss  on  May  7  to  9,  in  response  to  the  atmosphere  of  air  on  May 
7  to  9,  shows  that  the  contents  of  the  swimmer  must  have  been  largely 
hydrogen  gas.  The  prolongation  of  the  effect  for  another  day  is  probably 
due  to  air  in  the  water.     Changes  of  rate  are,  as  usual,  abrupt. 


28c%i^3   -  8       /5 


Fig.  9. — Chart  showing  loss  of  mass  of  gas  in  diver  in  lapse  of  days. 
Diffusion  of  oxygen  into  hydrogen. 

The  period  of  recovery,  however,  is  characterized  by  an  entirely  new  rate, 
viz, 

—  w  =  18  X  io~^g/day 

only  a  little  more  than  one-half  the  preceding  rate.     Hence 

K  =  o.44Xio~^° 

In  other  words,  the  new  rate  corresponds  to  a  diffusion  of  three  gases, 
hydrogen,  oxygen,  and  nitrogen,  and  is  characteristic  of  this  mixture.  The 
coefficient  is  the  smallest  observed,  but  the  final  period  of  steady  diffusion 
has  not  yet  been  reached. 


UQUIDS  AND  ALUED   EXPERIMENTS. 


31 


23.  Transpiration  of  Hydrogen  into  Air  Through  Water. — These  experi- 
ments, given  in  table  7  and  fig.  10,  are  a  sustained  repetition  of  the  work 
in  §11,  using  a  much  heavier  swimmer,  so  that  a  decrease  of  the  area  of 
diffusion  due  to  loss  of  gas  by  transpiration  may  not  occur.  The  curve,  as 
before,  is  remarkably  regular  and  partakes  of  the  qualities  of  the  earlier 
curve  (fig.  5).  The  initial  rate  is  —  w  =  7 1 X  io~*g/day  or  8.2  X  io~''g/sec., 
which  is  of  the  same  order  as  the  datum  of  table  2,  remembering  that  the 
constants  of  the  apparatus  are  slightly  different.  The  coefficients  of  trans- 
piration are,  since  a=  11.5  cm.^ (inside  area), 

A"  =11.5  cm.  2/t'"  =  9.ocm.  /  =  20.5  cm. 

and,  if  the  water  heads  be  taken  as  a  trial  gradient  for  comparison,  so  that 
dp 


dl 


—  549  dynes/cm. 


^=1.3X10" 


/c=  16X10' 


somewhat  larger  than  the  above  datum  (ife=i.i  X  io~^'),  the  difference, 
however,  being  of  the  same  order  as  the  irregularities  of  the  sectional  areas 
of  the  diffusion  columns  and  referable,  in  part,  to  the  values  of  h"  and  h'" 
involved.  There  is,  furthermore,  a  difference  in  the  mean  of  the  irregular 
temperatures.     Close  agreement,  therefore,  was  not  to  be  looked  for. 


cfycU~l^      Z4-     ^Jkyi-     9      W~~^      S      7$dia 


Fig.  10. — Chart  showing  loss  of  mass  of  gas  in  diver  in  lapse  of  days. 
Diffusion  of  hydrogen  into  air. 

The  final  coefficients  are  largely  subject  to  the  water  heads  under  which 
diffusion  takes  place.     We  may  therefore  write,  since 

—  »»  =  3-5Xio~®g/day  or  4.oXio""g/sec.  ^=0.64X10"" 

and  from  this 

K =0.78X10-^° 

which  approaches  the  coefficient  for  air  (0.91X10"^°),  as  would  be  antici- 
pated.    One  may  note,  however,  that  it  is  nevertheless  still  below  it. 


32 


THE   DIFFUSION  OF  GASES  THROUGH 


Table  7. — Diffusion  of  hydrogen  through  water  into  air.  Heavy  swimmer,  A/= 37.42 ; 
i?/,=4i.45Xio»;  pm=i3-6;  i  ^^,=0.3486;*  A  =  Mgpm/Rh  — 0.0120^;  h'=i.8  cm.; 
A"=  11.5  cm.;  A'"=4.5  cm.; /  =  20.5  cm.  Areas, inside  11. 5cm. 2,  outside  13.5  cm.*, 
ring  24.6—13.5=11.1  cm.-;  pa  =  89.55Xio~''.  Diameters  3.83,  4.15,  5.6  cm.;  cor- 
rection 0.13  cm.  Hg. 


Date. 

Hour. 

Barom-     „ 
eter.       ^ 

^ 

OTXIO* 

1 
Date. 

Hour. 

Barom- 
eter. 

H 

/ 

WXIO" 

A. 

m. 

0 

h. 

w. 

0 

Apr.  14 

5 

00 

76.26    74.00117.4 

2007 

May  10 

4 

00 

75  32 

43-7' 

21 .2 

1171 

15 

3 

00 

75.81 

71 .86    19.7 

'935 

1            " 

4 

00 

75 

69 

43 

48 

21.6 

1 164 

16 

3 

30 

7525 

68.92 

18.8 

1861 

\            12 

4 

00 

75 

90 

43 

37 

21.5 

1 161 

•7 

3 

30 

75-45 

65.96 

17.9 

1786 

I            >3 

4 

30 

75 

92 

43 

10  22.0 

1 1 52 

18 

4 

00 

75.67 

63.44 

18.3 

1715 

I            '4 

4 

30 

76 

81 

42 

75   20.6 

1 148 

«9 

4 

00 

75.69 

61 .02 

16.9 

1657 

1            '5 

4 

00 

76 

'4 

42 

28  20.2 

"37 

20 

3 

45 

75.10 

58.82! 16.2 

1601 

:        16 

4 

00 

75 

74 

42 

45I21.9 

"35 

21 

4 

00 

75  50 

57.21    16.8 

1554 

1        17 

4 

00 

75 

93 

42 

44|2i.9 

"35 

22 

4 

00 

76.14 

55.64! 16.7 

1512 

I        18 

4 

00 

75 

32   |42 

22   21 . I 

1132 

23 

4 

00 

76.37 

53-81 

16. 1 

1465 

1            '9 

4 

00 

75 

86 

42 

'321.6 

1 128 

24 

4 

00 

76.02 

52.65 

'7-4 

1428 

1           20 

4 

00 

76 

08 

42 

1 5   22 . 5 

1 125 

25   4 

00 

76.26    51.94 

18.5 

1404 

!           21 

4 

30 

76 

09 

42 

09  21 .9 

1 123 

26 

3 

30 

76.82     50.82:  18.4 

'374 

22 

4 

00 

75 

82 

4' 

97  22.4 

1121 

27 

3 

15 

76.88    50.09    19.7 

'349 

23 

4 

00 

76 

40 

41 

98  23.  1 

1118 

28 

3 

15 

76.33  '48.52 |20.8 

1302 

24 

4 

00 

76 

1 1 

4' 

79  22 . 6 

1115 

29 

4 

00 

75.77    I49.OI  ,21.2 

'3'3 

1           25 

4 

00 

75 

69 

4' 

81J23.3 

H13 

30 

4 

00 

75-58 

48.02    19.7 

1293 

26 

4 

00 

75 

96 

4' 

64 1 23 . 1 

1109 

May   I 

3 

45 

75.02 

47.31    20.2 

1272 

i           27 

4 

00 

76 

22 

4' 

3'  i22.5 

1 103 

2 

4 

00 

74-91 

46.71    20.0 

1257 

28 

4 

30 

76 

20 

4' 

14122.6 

1098 

3 

4 

00 

75-7' 

45.78    19.0 

'235 

!                  29 

4 

00 

75 

95 

40 

82  i  2  I  .  5 

1093 

4 

4 

«5 

76.14 

44 . 96    19.0 

1213 

30 

4 

00 

76 

22 

40 

73121.1 

1092 

5 

4 

00 

76-35 

44.33    18.2 

"99 

3' 

3 

30 

75 

9' 

40 

66121.6 

1088 

6 

4 

00 

76.48  (44.03  I  18.8 

1189 

June     I 

4 

00 

74 

96 

40 

88 

23.2 

1089 

7 

4 

30 

76.06 

43  85 

19.0 

1 183 

i             2 

5 

00 

75 

55 

40 

80 

23.2 

1087 

8 

4 

00 

75-93 

43.83 

20.2 

1178 

3 

3 

•5 

76 

25 

40 

56 

21 .9 

1085 

9 

4 

00 

74-95 

43-85 

21 . 1 

"75 

1 

*Cf.  §  24. 

24.  G)rrection  for  Density  of  the  Glass. — The  provisional  value  of  i/pg  ad- 
mitted in  tables  2,  3,  4,  5,  6,  and  7  when  the  divers  were  engaged,  viz, 
i/P(,  =  0.3486,  was  inadvertently  chosen  too  small;  i.  e.,  the  density  was 
overestimated.  Experiments  made  by  Miss  L.  C.  Brant  at  the  end  of  the 
work,  when  the  divers  were  available,  showed  the  values  given  in  table 
8,  the  divers  being  recognized  by  the  weights  m. 

Table  8. 


No. 

m 

Pa 

Used  in  table. 

A 

B 

C 

D 

12.01 14 
37.4248 
14.4481 
1 8 . 0962 

2.4840 
2.4701 

2.4873 
2.4219 

3.6 
7 
5 

2,4 

It  suffices  for  the  present  purposes  of  correction  to  take  the  mean  value 
p,=  2.466,  so  that  the  error  is  8pg  =  —0.402. 


UQUIDS  AND  AhhlHD  EXPERIMENTS.  33 

If  we  differentiate  the  equation 
logarithmically,  with  respect  to  p,  the  result  is 


Pm> 


P,(p,—pJ 

and  since  k  =  m/a{dp/dl),  the  same  relative  error  will  occur  in  m,  m,  v,  v,  k, 
and  K.  Since  p„=  i  (nearly)  and  the  assumed  value  of  p,= 2.868  and  5pj  = 
—  0.402,  this  correction  is 

—0.402 
2.868(1.868)  "~°-°^^ 

Unfortunately  the  error  5p,  is  too  large  to  admit  of  differentiation.  The 
correction  for  m  may,  however,  also  be  given  directly  by  multiplying  by 

i/Ptg-i/p» 

T^/Pt^—T^/Pt 

where  the  numerator  contains  the  correct  values.  In  this  way,  for  the 
mean  temperature  of  observation,  the  fraction  is 

0-S974 

l^'^  =1-0.0871 
0.6544 

or  the  correction  is  —8.7  per  cent.  It  will  therefore  be  necessary  to  reduce 
all  the  values  specified  by  this  amount.  It  is  needless  to  apply  the  cor- 
rection to  the  above  tables,  since  their  chief  purpose  was  to  show  the 
character  of  the  variation  of  m  in  the  lapse  of  time,  and  all  temperature 
corrections,  etc.,  have  there  been  made.  But  in  table  9  of  the  next  section, 
which  is  a  summary  of  essential  results,  the  correction  has  been  introduced 
in  full.     The  final  data  are  therefore  smaller  than  the  above. 

25.  Summary.  Relatively  Slow  Diffusion  of  Mixed  Gases. — The  data 
of  the  preceding  tables  have  been  brought  together  in  all  their  essential 
features  in  table  9,  values  in  parenthesis  being  nominal,  due  to  the  variable 
gas  constant,  R,  involved.  In  case  of  mixed  gases  the  initial  diffusion  is 
simply  tabulated  for  comparison  and  the  gradient  selected  (water  heads  h") 
merely  furnished  a  means  of  obtaining  a  datum  (^  or  k  in  parenthesis),  inde- 
pendent of  the  dimensions,  etc.,  of  the  apparatus.  In  these  cases  {k)  or 
{k)  have  no  immediate  meaning,  because  the  diffusion  is  differential  under 
conditions  which  have  not  been  disentangled.  The  data,  like  m,  which  is 
not  free  from  the  constants  of  the  apparatus,  merely  indicate  the  enor- 
mously rapid  diffusion  at  the  outset,  while  the  potential  energy  of  separated 
gases  is  being  expended.  In  case  of  mixed  gases  m  also  is  nominal,  the  true 
datum  being  v,  the  number  of  cubic  centimeters  diffusing  per  second  as 
explained  above. 


34 


THE   DIFFUSION   OF   GASES  THROUGH 


J3 
O 


oJ 

Vh 

3 

>l 

>. 

>. 

>-l 

>. 

>. 

>i 

CI 

^ 

"c 

c 

c 

c 

c 

c 

c 

"a 

U 

c 

a. 

o 

o 

o 

o 

o 

o 

o 

'•5 

•c 

CJ 

•a 

T3 

•o 

TJ 

T3 

-c 

-d 

u 

ni 

•r^ 

oJ 

n! 

cfl 

n! 

<A 

rt 

ctf 

• 

0 

C 

^ 

O) 

(U 

ID 

IL> 

W 

<L) 

o 

^ 

j: 

y 

s^ 

J= 

x: 

J! 

J3 

J3 

J2 

a 

Ih 

E 

u 

u 

i^ 

u. 

u 

u, 

u 

B 

a 

o 

w 

(U 

w 

(U 

a; 

OJ 

(U 

PS 

"S 

rt 

rt 

rt 

c8 

rt 

rt 

"S 

^ 

pq 

^ 

^ 

^ 

^ 

^ 

^ 

^ 

,,^^ 

,,-^ 

^^ 

,_^ 

,_^ 

— 

r) 

rTN 

H 

fS 

,__ 

^ 

^ 

■• — ^ 

"^-^ 

^ 

^ ' 

■S 

^- 

•— ' 

n 

rt 

.2 

^ 

,__, 

__, 

_ 

rt 

_^ 

^^ 

Pi 

n 
O 

■t-> 
O 

G 

c 

■^ 

rt 

"c 

'S 

'c 

S 

to 

s 

to 

'S 

to 

to 

23 

rr\        Tj- 

fS 

r« 

r>. 

r^ 

ITN 

^^^ 

ir\ 

l#N 

VO 

>o 

V£) 

fei5 

.^ 

,,^ 

^_^ 

,_ 

^_^ 

^_^ 

^  =>        w 

y^^ 

-     00 

fe2>,i 

PTs            l/> 

«H 

»— 

-<- 

— 

O 

CO 

0\ 

0\                ~ 

o 

!-•- 

ir\ 

t^ 

(^ 

•<i- 

0  ^        £^ 

o 

-^ 

-<1- 

_■ 

CJ 

^-' 

~— ' 

' 

"■ 

,„ 

,— . 

,_^ 

,_^ 

* 

* 

S           V 

■— 

-* 

^ 

oo 

•— 

00 

■<*■ 

2  >.£ 

Cn 

o 

o 

l^ 

O 

\0 

00 

r- 

-"f 

X«^ 

O 

r« 

n-i 

vd 

Tf- 

_ 

^— 

v_^ 

'-^ 

■— ' 

•a 

,„ 

.'-^ 

,_^ 

,_^ 

^.^ 

,-^ 

,,^ 

«5r,      J? 

lr^ 

"tj  "o  rt 

l/N 

o 

00 

fcX^ 

O 

r^ 

oc 

ON 

ir\ 

0^ 

ir\ 

O 

— 

C^        O 

o 

\r\ 

00 

Os 

o-«  ^ 

o    « 

- 

'    ^ 

-^ 

^ 

^ 

-- 

^ 

^„ 

/—v 

^ , 

,_^ 

^^ 

,_^ 

^^ 

~          1 

EJj 

4#> 

21 
X 

(S 

k« 

■"I- 

a^      o^ 

r^      — 

o 

vo 

t^ 

M- 

o 

— 

o 

o 

ro 

o 

o 

ON 

o 

S>. 

„ 

^ 

^ 

vo 

J^ 

PQ 

"— 

'     — - 

"— ' 

^-' 

"^ 

'—" 

•go  m 

^ 

ir\ 

§ 

o 

0*^ 

ITS 

t^ 

t^ 

ir> 

rrs 

ro 

VO 

ir\ 

m        (S 

o 

o 

•^ 

00 

r'^ 

■* 

fS 

ir\ 

ri 

— 

fcX"; 

O 

— 

r^      t^ 

G\ 

o 

-^ 

— 

O 

o 

'O 

O 

O 

O      '^ 

O 

J 

%  ^ 

■*       r^ 

t^      r^ 

VO 

o\ 

rr\ 

O 

0\ 

ir\ 

ITN 

00 

O 

r<-s        p<^ 

VC 

^ 

G^ 

•^ 

rrs 

\jr\ 

-^ 

rs 

— 

(S 

t— 1 

X"^ 

O 

— 

r^       t^ 

C\ 

o 

ITS 

— 

o 

O 

C^ 

o 

o 

O 

■0  = 

0\        rr\ 

~^ 

.    ^ 

— 

't-^ 

--- 

--- 

-- 

--- 

— 

— 

--- 

•So  o 

\0          o 

oc 

00 

I>. 

rr\ 

o 

00 

■<1- 

Tf 

t^ 

^ 

Tf 

C\ 

2x1 

00 

J-gbC 

1 

1 

^ 

i. 

J^ 

\^ 

+ 

J^ 

^ 

\^ 

^ 

^ 

^ 

•^          rr\ 

~ 

.        .^ 

-- 

'o 

— 

'-- 

--- 

— 

— 

'- 

•-- 

"o    CJ 

O 

— 

rr\        rr\ 

r« 

Tl- 

o 

o 

c^ 

o 

o 

r^ 

•- 

x^ 

■^        - 

VO 

vo 

00 

4 

00 

tr\ 

m 

lA 

rr\ 

fi 

VO 

C^ 

.gbe 

1 

1 

J^ 

-1 

J^ 

J^ 

+ 

J^ 

J__ 

J^ 

\^ 

^ 

J^ 

c 

c 

d 

s  . 

be 

bo 

bo 

■ti   ^ 

o 

o 

o 

0  o 

u 

u 

u 

£•§ 

"O 

•o 

•a 

O 

>. 

a 

Ih 
< 

>> 

>> 

u 

d 

c 

<L 

C     . 

bo 

b. 

) 

H 

e| 

O 

c 

U 

£•§ 

bO 

._^ 

U 

>, 

1 

>-• 

X 

< 

W 

t 

< 

O 

UQUIDS  AND   Al,UED   EXPERIMENTS.  35 

The  case  of  hydrogen,  diffusing  into  air,  does  not  show  large  values  in  m; 
this  might  seem  to  be  due  to  an  even  more  rapid  diffusion  during  the  first 
day,  decaying  more  rapidly.  It  is,  however,  at  once  interpreted  on  reduc- 
ing m  to  V,  the  diffusion  relative  to  volume  (see  table  9). 

The  initial  diffusion  of  hydrogen  out  of  the  swimmer  into  air,  and  of 
hydrogen  into  the  swimmer  containing  air,  is  in  excess  of  the  opposed 
current  of  air,  by  an  amount  of  about  the  same  order.  The  rate  at  which 
imprisoned  hydrogen  escapes  from  the  swimmer  in  excess  of  the  entrance 
of  air  is,  however,  definitely  larger  than  the  excess  of  rate  of  entry,  compared 
with  the  escape  of  air  in  the  converse  case,  for  reasons  which  do  not  at  once 
appear.  These  rates  are  t;  X  10*  =  8  to  10  for  escaping  hydrogen,  and 
z;Xio®  =  5  for  entering  hydrogen,  and  are  to  be  somewhat  modified  by  the 
constants  of  the  apparatus.  Possibly  the  fact  that  the  water  must  first  be 
saturated  with  hydrogen  before  this  gas  can  enter  the  swimmer,  whereas  it 
escapes  with  greater  freedom  into  unsaturated  water,  accounts  for  this  initial 
difference.  At  the  same  time,  hydrogen  enters  the  swimmer  against  the 
pressure  gradient  of  the  water  levels. 

In  general,  however,  the  diffusion  of  mixed  gases,  during  the  first  day, 
is  in  need  of  more  detailed  investigation,  in  which  case  special  methods  of 
charging  and  of  observing  without  removing  the  artificial  atmosphere,  will 
have  to  be  devised,  as  is  done  in  the  last  chapter. 

The  special  feature  of  table  9  is  the  relatively  low  rate  of  the  final  diffu- 
sion of  mixed  gases.  Thus  the  mixture  air-hydrogen  (table  8),  which  is 
nearly  all  air,  shows  a  lower  rate  than  pure  air;  the  final  hydrogen-air 
diffusion,  which  is  nearly  all  hydrogen,  a  lower  rate  than  pure  hydrogen; 
the  final  hydrogen-oxygen  diffusion,  a  much  lower  rate  than  pure  hydrogen ; 
the  hydrogen-oxygen-nitrogen  diffusion,  which  is  nearly  all  hydrogen,  a 
much  lower  rate  than  air  or  hydrogen,  etc.  It  seems,  therefore,  that  small 
quantities  of  a  second  gas  added  to  the  pure  gas  markedly  reduce  its  rate 
of  diffusion,  k.  The  reason  of  this  would  seem  to  be  the  potential  energy 
of  the  mixture,  which  must  here  be  increased  to  the  potential  energy  of 
separated  gases.  Thus  the  opportunity  of  dissipating  potential  energy  is 
decreased  and  the  diffusion  is  correspondingly  sluggish. 

It  is,  however,  probably  sufficient  to  refer  the  whole  question  to  the  actual 
value  of  the  full  pressure  gradients  involved,  ^i  Pa>  Pb>  Pc  •  •  •  »  ^^^  ^^^ 
partial  pressures  of  the  gases  within  the  swimmer,  when  B  is  the  barometric 
pressure  and  h"p„g  the  pressure  due  to  the  heads  of  water  bearing  on  the 
gas  mixture  and  tt  the  vapor  pressure, 

Pa+Pi,-^Pc+   •   '   '    =B-ir^h"p„g 
Hence  if  the  pressure  B  —  w  is  due  to  the  gas  a  (artificial  atmosphere),  it 
will  enter  the  swimmer  if 

Pi-\-pc+  '  '  •   >h"p„g 

it  can  not  escape  from  the  swimmer  until  pb+pe-i-  '  '  '   —^"Pv>&-     -^s  this 
is  a  small  pressure,  the  gases  b,  c,  .  .  .  must  themselves  escape  slowly. 


36 


THE)   DIFFUSION   OF   GASSS  THROUGH 


and  consequently  the  gas  a,  with  the  diminution  of  p^-\-pg-}-  •  •  •  will  also 
escape  slowly.  As  a  whole  the  results  contain  a  remarkably  striking  com- 
mentary on  the  meaning  and  potency  of  the  pressure  gradient.  To  develop 
an  equation,  however,  which  embodies  all  these  facts,  in  such  a  way  as  to 
predict  the  observations  quantitatively,  has  not  been  accomplished  in  the 
above  paper.     In  fact,  if  we  write 

•  ,    •       •  ,   •  mo-\-fntdt 
m  =  pv-tvp  =  pv-\-  p  ■ 


where  Wois  the  initial  charge  of  pure  gas,  m  and  v  are  given  in  terms  of  p  by 
equations  (31)  and  (35).  Hence  the  equation  may  be  expressed  in  terms 
of  p  and  becomes  eventually 

—  (pv  —  m)  —  2pv  —  (pv  —  m)  =0 
P 

Tabus  10. — ^Values  of  p  (density)  in  the  final  diffusions  of  mixed  gases.     B  —  t  =  74  cm. ; 
n  =  987,000-1- />' dynes;  ^0=109X10-";  feft=  i. 92X10-'*;  i?ft/i?a=  14.44. 

I) 


From 
table  7. 

From 
table  5. 

mXio" 

P.Xio« 

a 

0.40 

82 

H.5 

20.5 

11.5 

11,260 

998,500 

14.27 

0.987  (air) 

5-9 

1,200 

6.4 

20.0 

10.0 

9.790 

997,100 

0.0864 

0.981  (hydr.) 

/ 

h" 

p' 

n 

p/Pt 

X 

Here  v  and  m  involve  p,  while  t"  and  m  are  proportional  to  p.  Moreover,  the 
phenomenon  expressed  in  terms  of  p,  the  density  of  the  imprisoned  gas, 
should  be  integrable,  but  the  equation  does  not  seem  to  reduce  down  suffi- 
ciently to  make  the  attempt  at  integration  worth  while. 

With  regard  to  equations  (31)  or  (35)  it  should  be  pointed  out  that  when 
m  or  V  is  known,  p  may  be  computed  in  terms  of  the  coefficients,  k^  and  k^, 
of  the  two  gases  diffusing  into  each  other.  As  in  the  final  phases  of  the 
phenonemon  m  is  nearly  constant,  the  density  and  hence  the  composition 
of  the  gas  undergoing  diffusion  in  one  direction  may  be  found  with  some 
precision.  Thus  in  table  9  the  air-hydrogen  and  hydrogen-air  diffusions, 
when  m  has  become  constant,  correspond  to  mixed  gases  of  the  density  and 
composition  indicated  in  table  10. 

The  marked  irregularities  of  the  graphs  in  case  of  air  and  oxygen,  when 
there  are  temperature  variations,  has  been  referred  to  the  effect  of  solution, 
which  absorbs  a  soluble  gas  at  falling  temperatures  and  rejects  it  at  rising 
temperattues,  contemporaneously  with  the  occurrence  of  diffusion.     It  is 


LIQUIDS  AND  ALLIED   EXPERIMENTS.  37 

nearly  absent  in  case  of  the  diffusion  of  hydrogen  and  is  thus  not  a  direct 
temperature  effect.  To  state  the  case  analytically,  the  volume  v  of  the 
imprisoned  gas  is,  in  terms  of  its  gas  constant  R,  absolute  temperature  t, 
pressure  p,  and  mass  m,  as  usual  given  by 


p  =  R—T  =  RpT 

V 


Now,  since 


it  follows  that 


Kt 


P 

where  v  is  the  volume  which  would  be  contained  in  the  diver  and  p  the 
corresponding  density  of  the  gas,  at  any  selected  fixed  or  fiducial  atmos- 
pheric pressure  and  absolute  temperature  p  and  t,  under  which  the  experi- 
ment is  supposed  to  take  place.  If  the  latter  be  given  in  centimeters  of 
mercury,  the  barometric  height  being  B, 


H      /I        i\ 


It  follows  that  if  we  divide  m  by  p,  the  density  of  the  gas  originally  in  the 
diver  under  the  specified  normal  conditions  (density  being  known  for  a  single 
gas  but  not  at  once  given  in  case  of  a  mixture),  we  refer  all  data  to  these 
conditions  and  temperature  and  pressure  discrepancies  are  excluded.  More- 
over, V  and  the  corresponding  diffusion  coefficient,  k  =  v/a(dp/dl),  can  be  com- 
puted for  any  gas,  mixed  or  simple.  Under  the  form  Bv/H-\-M/pg  =  M/p„, 
the  above  volume  equation  is  obvious  directly,  as  the  approximate  condi- 
tion of  flotation  at  the  manometric  pressure  H. 

Finally,  it  is  not  improbable  that  the  irregularities  of  graph  in  question 
may  be  actually  used  as  a  means  of  measuring  the  variation  of  the  solu- 
bility of  a  gas  in  the  liquid,  with  temperature. 

In  conclusion  I  may  point  out  the  extreme  sensitiveness  of  the  above 
method.  With  the  same  apparatus,  relative  data  should  be  determinable 
w^ith  an  accuracy  comparable  to  that  with  which  the  barometer  can  be  read; 
i.  c,  much  within  o.i  per  cent,  since,  finally,  v  =  v'H/B,  where  v'  is  the  nearly 
constant  volume  on  flotation.  Absolute  data,  however,  require  a  determi- 
nation of  the  constants  of  the  apparatus,  which  is  less  accurately  feasible. 
It  has  already  been  intimated  that  to  secure  this  sensitiveness,  temperature 
must  be  kept  constant  in  the  lapse  of  time.  Furthermore  the  rigorously 
pure  gases  must  be  introduced  under  their  own  atmospheres  and  there  must 
be  no  foreign  gases  dissolved  in  the  liquid.  Moreover,  all  observations 
must  be  made  with  the  artificial  atmosphere  kept  in  place.  Indeed,  it  is 
a  question  whether  the  effect  of  diffusion  in  rendering  gases  stored  over 
water  impure  has  generally  been  adequately  guarded  against. 


CHAPTER  III. 

HYDROSTATIC  METHODS  FOR  THE  ABSOLUTE  ELECTROMETRY 
OF  HIGH  POTENTIALS. 

Part  I. — Hydrometer  Methods. 

26.  Introduction. — The  remarkable  precision  of  weight  measurement, 
which  was  shown  in  case  of  the  experiments  with  the  Cartesian  diver  dis- 
cussed in  the  above  chapters,  suggested  experiments  along  similar  lines  for 
purposes  where  other  forces  (electrical  forces,  for  instance)  are  in  question. 
It  will  be  necessary  in  the  course  of  the  present  work  to  measiu-e  very  high 
potentials.  Hence  the  modification  of  the  absolute  electrometer  in  such  a 
way  that  the  movable  disk  is  supported  by  a  hydrometer,  or  by  a  Cartesian 
diver,  floating  in  insulating  liquids  under  known  conditions,  seemed  to  be 
an  interesting  application.  In  fact,  the  direct  test  of  the  consequences  of 
Coulomb's  law,  for  the  case  in  which  the  movable  conductor  is  a  Cartesian 
diver,  is  well  worth  the  trial. 

27.  Absolute  Electrometer. — The  first  experiments  were  made  by  the 
hydrometer  method,  and  figs,  ii,  12,  13  show  the  apparatus.  In  fig.  11  a 
ceded  is  the  condenser,  dd  being  the  guard  ring  and  e  the  movable  disk,  both 
being  flanged  on  the  circular  edges  toward  each  other,  for  stiff"ness.  The 
plate  ee  is  supported  by  the  screw  55  passing  through  the  lateral  arm  of  hard 
rubber  h.  The  hard-rubber  handle  a  rotates  the  screw  ss  and  plate  cc 
around  the  vertical  axis,  so  that  it  may  be  brought  in  contact  with  dd  or 
removed  from  it  by  as  much  as  may  be  desirable.  The  complete  and  partial 
turns  of  ss  are  given  by  a  graduated  head  (not  shown)  as  in  case  of  the  ordi- 
nary micrometer  caliper.  In  this  way  the  distance  apart  D  of  the  plates 
cc  and  dd  is  sharply  determinable. 

In  certain  of  the  measurements  below  it  is  desirable  to  be  able  to  raise 
the  guard  ring  from  its  position  in  the  uncharged  apparatus  to  the  level  of 
the  disk.     It  should  therefore  be  adjustable  in  the  vertical  direction. 

The  guard  ring  dd  is  the  top  of  a  box  and  is  perforated  at  its  bottom  with 
a  brass  tube  ggg,  35  to  40  cm.  long,  closed  by  the  plug  k.  The  T-coupling 
//  communicates  at  i  with  a  water  reservoir  for  floating  the  hydrometer, 
the  top  of  which  is  the  disk  e. 

In  fig.  1 1  A  the  float  is  a  very  thin  tube  of  aluminum  ff  about  0.854  cm. 
in  diameter  and  nearly  30  cm.  long.  It  is  closed  above  and  below  and  there 
prolonged  by  a  thin  stiff  wire  m  about  7  cm.  long,  terminating  in  the  brass 
sinker  n.  The  whole  arrangement  efmn  weighs  about  15  grams  and  floats 
with  the  tube  vertical  and  disk  horizontal  in  the  charge  of  water  ww.  This 
float  is  very  mobile  in  the  vertical  direction,  so  that  if  electrical  forces  are 
strong  enough  it  may  actually  be  lifted  into  contact  with  the  disk  cc.  One 
of  the  methods  of  measurement  presently  to  be  given  will  depend  upon  this 
possibility. 

39 


40 


THE   DIFFUSION  OF  GASES  THROUGH 


To  keep  the  water  level  at  the  proper  height  or  to  raise  or  lower  it  by  a 
definite  amount,  the  screw  pump  in  fig.  13  is  available.  This  consists 
essentially  of  a  thick  screw  6'  playing  into  the  brass  tube  cc,  which  is  closed 
at  the  top  by  the  stuffing  box  a  compressing  the  ring  of  soft  material  Ih. 
The  bottom  of  the  tube  cc  ends  in  the  tubulure  i,  to  be  joined  by  appro- 
priate tubing  with  the  corresponding  tubulure  i  in  fig.  11  a.  The  brass 
tube  cc,  fig.  13,  is  quite  filled  with  water  to  the  exclusion  of  air,  so  that  ever}' 
turn  of  the  screw  5  raises  the  level  vjw  in  fig.  11  a  by  a  definite  amount. 
The  screws  is  also  provided  with  a  graduated  head  (not  shown),  so  that  the 
whole  turns  and  fractions  of  a  turn  may  be  read  off,  and  the  ratio  of  the 
diameter  of  the  water  level  in  fig.  11  a  and  that  of  the  screw  5  in  fig.  13 
must  be  known.     In  the  figure  the  ratio  of  the  areas  is  about  ten  to  one. 


n 


Fig.  II  A. — ^Absolute'electrometer  with  disk  carried  by  tubular  hydrometer  of  aluminum. 
B. — Absolute^electrometer  with  glass  U-tube  for  adjusting  levels. 


It  is  interesting  to  note  in  passing  that  on  sudden  advance  or  retreat  of 
the  screw  S  an  impulsive  wave  passes  through  the  liquid,  suddenly  raising 
and  lowering  the  disk  e  often  more  than  a  centimeter  and  with  considerable 
force.     Direct  and  reflected  waves  are  recorded  in  this  way. 

In  many  of  the  experiments  it  was  found  sufficient  to  coat  the  screw  (hot) 
with  an  adhesive  layer  of  resin  and  beeswax.  A  v/ell-fitting  brass  screw 
0.75  inch  in  diameter  and  20  threads  to  the  inch  was  used.  A  socket  of 
indurated  fiber  is  even  preferable,  there  being  no  appreciable  leakage  for 
$ome  time.    This  avoids  the  complication  of  a  stuffing  box,  but  of  course  it 


LIQUIDS  AND  AI^LIED  EXPERIMENTS. 


41 


will  not  last  indefinitely.  In  other  experiments  the  hose  ii  was  branched 
and  led  to  a  glass  reservoir,  showing  the  water  level  on  the  U-tube  principle. 
In  such  a  case  the  water  level  w  could  be  read  off  at  the  reservoir,  by  a  cathe- 
tometer  or  some  equivalent  simpler  attachment. 

In  the  latest  form  of  apparatus  the  guard-ring  cup  holding  the  water  at  w 
was  dispensed  with  and  replaced  by  the  prolonged  tubeg  (now  made  of  glass) 
as  shown  in  fig.  jib.  Here  gg  is  the  glass  tube  0.75  to  i  inch  in  diameter 
communicating  with  the  hose  i  below  and  holding  the  float  /  submerged  as 
far  as  the  water  level  iz>.  The  advantage  of  this  form  is  this,  that  all  parts 
of  the  floating  tube  may  be  seen  and  the  floating  level  read  off  at  v,  for 
instance.  It  is  necessary,  however,  to  keep  the  tube  in  the  middle  of  the 
water  level,  at  w,  by  aid  of  three  horizontal 
adjustment  screws  (not  shown),  at  a  hori- 
zontal angle  of  1 20°,  surrounding  the  tube 
ff  very  loosely.  In  such  a  case  the  disk  e 
is  kept  centered,  the  tube  /  is  never  in 
contact  with  gg,  and  a  little  tapping  obvi- 
ates all  danger  of  friction. 

Fig.  II B  also  shows  the  level  controlled 
by  a  tubular  glass  receiver  hh  with  its 
water  level  visible  at  w\  This  is  to  be 
held  on  a  vertical  slide  micrometer,  so 
that  the  shift  of  hh,  due  to  a  charge  on  cc, 
may  be  accurately  read.  In  fact,  this  form 
of  instrument,  requiring  no  subsidiary 
apparatus,  was  finally  adopted  throughout. 
The  vertical  slide  h  need  only  be  a  few 
centimeters  long  and  provided  with  a  moving  vernier  for  a  fixed  scale. 

For  potentials  higher  than  20,000  or  30,000  volts,  the  vertical  height  of 
the  space  cd  must  be  much  increased,  to  prevent  the  continuous  rise  of  the 
disk  ee.  Hence  the  guard  ring  should  be  much  larger  than  in  the  figure  or 
the  disk  appreciably  smaller.  Furthermore,  in  this  case  the  sharp  screw 
55  and  similar  sharp  edges  elsewhere  as  in  the  disks  cc,  dd,  etc.,  are  inadmis- 
sible. Without  rounded  edges  and  a  rounded  screw,  the  secondary  dis- 
turbances due  to  electric  winds  interfere  with  the  interpretation  of  the 
measurements  and  the  apparatus  will  not  take  a  high  potential.  All  parts 
except  the  disk  cc  are  of  course  put  to  earth,  and  possible  induction  between 
cc  and  other  conductors  except  dd  must  be  scrupulously  guarded  against. 

Finally,  fig.  12  shows  an  alternative  float  consisting  of  the  disk  e  corre- 
sponding to  fig.  1 1  A,  the  tube  ff  passing  the  preferably  conical  capsule  pp 
about  1.5  cm.  high  and  5  cm.  in  diameter,  of  thin  brass  hermetically  sealed. 
The  tube  ff  is  prolonged  below  by  the  solid  brass  rod  n  or  sinker.  When 
placed  in  the  cup,  fig.  1 1  a,  or  in  a  similar  vessel,  the  water  level  is  at  ww 
and  may  be  adjusted  by  dropping  small  weights  down  the  tube  ff.  The 
same  method,  fig.  13,  is  used  for  placing  this  level.    The  whole  arrangement 


Fig.  12. — Hydro- 
meter and  disk 
carried  by  air- 
chamber. 


Fig.  13. — Com- 
pression screw 
for  adjusting 
levels. 


4S  THE  DIFFUSION  OP  GASES  THROUGH 

weighs  about  35  grams,  including  disk  and  sinker.  The  essential  part  is 
the  tube//  of  copper  about  0.5  cm.  in  diameter.  This  float  is  not  intended 
to  rise  and  fall  as  in  the  case  of  fig.  1 1  a,  but  to  move  to  a  definite  level 
under  the  influence  of  the  electrical  forces  of  the  condenser. 

Water  has  been  referred  to  as  the  liquid  charge  of  the  apparatus.  It  has 
an  advantage,  inasmuch  as  the  whole  of  the  lower  half  of  the  condenser  may- 
be earthed  and  the  guard  ring  and  disk  are  necessarily  at  the  same  potential. 
It  has  the  very  serious  disadvantage,  however,  that  large  capillary  forces 
are  involved,  particularly  in  case  of  the  wide  stem  of  fig.  11  a.  Hence  a 
charge  of  kerosene  oil  or  even  of  the  hea\der  clear  paraffin  oil  is  preferable. 

In  cases  where  the  disk  e  in  its  uncharged  position  is  to  be  flush  with  the 
surface  dd,  it  is  convenient  to  provide  the  tube  gg  with  opposite  glass  win- 
dows (not  shown),  through  which  a  mark  on  the  tube//"  or  the  bottom  of 
the  tube  or  the  sinker  may  be  distinctly  seen.  The  adjustment  is  made 
once  for  all,  so  that  when  e  is  flush  with  d,  the  mark  seen  at  the  window  may 
coincide  with  a  definite  line  or  two  lines  in  the  same  horizontal  plane  on 
the  opposed  windows. 

28.  Equations  for  the  Tubular  Float. — Let  V  be  the  diff"erence  of  poten- 
tial of  the  plates  of  the  condenser  in  the  absolute  electrometer  and  D  their 
distance  apart.  Let  F  be  the  electric  field,  so  that  F  =  V/D.  Further- 
more let  fg  be  the  electric  pressure  between  the  plates,  i.  e.,  the  pull  per 
square  centimeter. 

Suppose  the  disk  e  is  raised  a  small  distance  /  above  the  level  just  char- 
acterized by  D.     Then  we  may  write,  since  8^(300)^  =  2.262  X 10® 

/,=  F72.262Xio«X(I>-/)'  (i) 

if  V  is  given  in  volts. 

The  total  mechanical  force  evoked  by  the  same  rise  /  above  the  position 
of  equilibrium  of  the  float  is  vpg,  where  v  is  the  volume  of  the  stem  sub- 
merged, p  the  density  of  the  liquid,  and  g  the  acceleration  of  gravity. 
Let  r  be  the  radius  of  the  stem  (//,  fig.  11  a),  and  R  the  radius  of  the  disk 
{e,  fig.  II  a).  Then  the  amount  of  force  evoked  per  square  centimeter  of 
the  disk,  i.  e.,  the  mechanical  or  restoring  pressure  /„,  is 

fm=-^  hg  (2) 

In  the  case  of  equilibrium  these  two  pressures  are  equal,/,  =/^,  and  there- 
fore 

V  =  2.262Xio'(£)pgiD-l)H  (3) 

To  measure  V,  therefore,  both  D,  the  original  distance  apart  of  the  un- 
charged plates  of  the  condenser  (disk  flush  with  the  level  of  the  guard  ring) 
and  the  rise  of  the  disk,  /,  on  charging,  must  be  known.  It  will  also  be 
desirable  to  raise  the  guard  ring  to  the  level  of  the  disk  in  the  charged 
apparatus. 


LIQUIDS  AND  AI^IylED  EXPERIMENTS.  43 

Since  equation  (2)  is  linear  in  /  and  equation  (i)  quadratic  in  /,the  curves 
of /j  and/„  in  terms  of  /  must  in  general  intersect  in  two  points,  one  of  which 
(lower  or  smaller  /)  corresponds  to  stable  and  the  other  (upper  or  larger  I) 
to  unstable  equilibrium  of  the  disk.  For  a  fixed  value  of  D  these  are 
further  apart  as  V  is  smaller.  When  V  increases  sufficiently  the  two  points 
of  intersection  eventually  coalesce  in  a  single  point.  This  particular  value 
of  /  shows  the  highest  stable  position  which  the  disk  may  reach.  For  large 
values  of  V  there  is  no  point  of  intersection,  or  the  disk  passes  without 
interruption  from  the  lower  to  the  upper  plate  of  the  condenser.  The  same 
result  may  be  brought  about  by  decreasing  D  for  a  fixed  V,  and  on  this 
principle  I  have  based  the  following  method  of  measurement. 

If  we  differentiate  equations  (i)  and  (2)  with  respect  to  /  the  results  are 

^*  = iK! u) 

dl       2.262Xio\D-lf  ^^* 

-di-R^PS  (5) 

If  these  slopes  are  identical 

V'=- 2.262X10' ^,Pg{D-iy  (6) 

2  K 

Now,  when  there  is  but  a  single  point  of  intersection  (tangency  of  equations 
(i)  and  (2)),  equations  (3)  and  (6)  correspond  to  the  same  value  of  /  =  /«, 
whence  after  canceling  superfluous  quantities 

D^3lc  (7) 

In  other  words,  if  the  electrical  forces  are  sufficiently  strong  to  raise  the 
disk  e  more  than  one-third  of  the  distance  D  between  the  plates  of  the 
condenser,  it  will  pass  all  the  way  to  the  upper  disk  cc.  Hence  under  these 
circumstances  equation  (3)  gives 

F'^  =  o.5027XioV='Z)V^'  (8) 

Thus  in  case  of  the  first  method  of  measurement  the  upper  plate  cc,  fig.  11  a, 
is  to  be  gradually  lowered,  while  the  disk  e  rises,  until  the  last  position  of 
stable  equilibrium  is  just  exceeded,  or  the  disk  travels  to  the  upper  plate. 
The  guard  ring  may  now  be  raised  D/^  and  a  closer  adjustment  made. 

29.  Constants  of  the  Tubular  Float. — To  show  the  numerical  relations 
involved,  the  values  of  /„  and  fg  may  be  computed  and  represented  graph- 
ically in  terms  of  the  lift  /.  Since  for  water  p=i,  and  the  diameters  of 
stem  and  disk  are  0.854  cm.  and  6.65  cm.,  respectively, 

fm=^  Pgl  =16.18/  dynes 
which  is  the  oblique  line  through  the  origin  of  the  graph  in  fig.  14. 


44 


THB   DiFlfUSION   OF  GASES  THROUGH 


To  compute /g,  a  suitable  value  of  D  and  F  must  be  assumed.     Let  D  =  4 
cm.  and  F  in  succession  lo^  io^Xi.41,  io^Xi.86,  io*X2  volts.     Since 

/,=  772.262X10^(4-0' 

the  successive  curvilinear  lines  of  the  diagram  are  obtained.  The  lowest 
have  two  intersections  each;  the  one  corresponding  to  stability  being  at  5 
and  the  unstable  one  at  us.  For  at  s,  a  lowering  of  the  disk  means  an 
excessive  upward  electric  force,  while  any  rise  of  the  disk  means  an  excessive 
downward  and  mechanical  force.  Just  the  reverse  is  true  at  us.  The  two 
upper  curves  have  one  contact  and  no  contacts,  respectively.  Hence,  when 
F=io^Xi.86  and  2^  =  4,  the  disk  will  just  be  on 
the  point  of  rising  without  interruption.  The  maxi- 
mum rise  compatible  with  stability  would  be  4/3 
cm.  The  rise  for  F=  10*  and  io^Xi.41  would  be 
roughly  0.18  and  0.43  cm.,  respectively. 

To  compute  the  potential  of  the  maximum  point  of 
stability  for  0  =  3^  =  4,  equation  (3)  becomes 

^2 
F' =  2.262  X 10' -r^  pg  —  Z)^=  1.86X10^  volts. 


K 


27 


The  values  of  /  for  the  stable  positions  of  the  disk  in 
case  of  different  values  of  D  and  F  are  not  so  easily 
found,  in  view  of  the  cubic  equation  (3).  When  / 
is  very  small,  however,  i.  e.,  for  values  of  F  less 
than  10^  volts,  I  may  be  neglected  in  comparison 
with  D  and  the  equation  becomes 


Fig.  14.— Chart  showing 
the  forces  actuating 
disk  for  different  po- 
tential differences  and 
displacements  of  disk. 


F=^  =  2.262Xio';^PgD'/ 


(9) 


Hence,  if  F=io^  the  disk  would  only  rise  about  0.018  centimeter.  For 
F=io2  to  0.00018  cm.,  etc.,  so  that  even  the  interferometer  could  not 
indicate  more  than  about  10  volts.  If,  however,  D  is  also  reduced,  say  to 
0.5  cm.,  or  8  times,  the  rise  will  be  /  =  0.0000092  cm.  per  volt;  for  D  =  o.i 
cm.,  /  =  0.001 15  cm.,  etc. 

Hence  with  the  use  of  the  interferometer  and  small  values  of  D,  there  is 
no  reason  why  ultimately  single  volts  should  escape  measurement  except 
for  the  capillary  forces  involved  in  flotation,  where  the  stem  penetrates  the 
liquid,  as  in  case  of  the  above  apparatus.  By  decreasing  the  diameter  of  > 
the  stem,  however,  as  in  the  float  fig.  12,  sensitiveness  may  be  further 
increased. 


30.  G)nstants  of  the  Conical  Float  (Capsule). — When  the  float  is  of 
the  form  given  in  fig.  12  and  a  suitable  \\'indow  is  provided  in  the  tube  gg, 
fig.  1 1  A,  or  other  vessel,  so  that  the  zero  position  (disk  e  flush  with  the 
guard  ring  dd)  may  be  accurately  determined  by  lens  or  telescope,  another 


I.IQUIDS  AND  ALIylKD  EXPERIMENTS.  45 

method  of  measurement  may  be  tested.  In  this  case  D  is  to  be  the  same 
for  the  charged  and  the  uncharged  state,  i.  e.,  to  be  constant,  while  the 
water  level  ww  is  lowered  in  fig.  1 1  a  by  a  definite  amount  of  rotation  of  the 
screw  in  fig.  13.     Hence  equation  (3)  becomes 

V^  =  2. 262X10^— ^PgW  (10) 

K 

where  /  is  the  drop  of  the  water  level  due  to  the  play  of  the  screw  5  in  fig.  13. 
If  2R'  is  the  diameter  of  the  water  level  ww,  in  the  cup,  fig.  11  a,  and  2R" 
the  effective  diameter  of  the  screw  (diameter  of  the  solid  cylinder  plus  the 
thickness  of  the  thread),  and  L  its  longitudinal  displacement,  equation  (10) 
becomes 


V' 


/  r  R"\  2 
=  2.262  Xio«(^--^j   pgLD-" 


If,  therefore,  {R" /R'Y  is  small,  say  o.i,  the  apparatus  is  correspondingly 
more  sensitive,  a  result  which  is  further  enhanced  by  making  {r/R^  small, 
i.  e.,  using  a  smaller  stem  and  larger  disk. 
In  case  of  the  given  float  actually  constructed 

2f  =  0.605  cm.         2i?  =  6.65cm.        2i2'  =  8.23  cm.        2i2"=  1.803  cm. 

so  that  for  water 

F^  =  2.262X  io«(^^^^^^V98iZ}^X  =o.879Xio''Z)=^i: 
\  6.65X8.23  J   "^ 

31.  Experiments  with  the  Tubular  Float. — Experiments  with  a  tubular 
float,  chiefly  in  the  form  fig.  iib,  were  made  at  considerable  length, 
but  only  a  few  results  need  here  be  recorded.  With  the  apparatus  as 
shoAvn  it  was  not  convenient  to  go  above  30,000  volts,  and  even  with 
this  voltage  the  inconstancy  of  the  electrical  machine  was  an  ever-present 
annoyance.  The  chief  purpose  of  the  table,  therefore,  is  to  show  the  rela- 
tive values  of  I,  the  depression  of  the  water  level  for  a  distance  apart  D  of 
the  disks  of  the  condenser,  when  the  upper  disk  was  at  a  potential  of  V 
and  the  lower  at  a  potential  zero. 

The  measurements  as  a  whole  proceeded  smoothly,  the  only  difficulty 
being  the  control  of  the  electrical  machine.  The  endeavor  to  increase  the 
potential  of  the  electrometer  above  35,000  volts  did  not  succeed,  while  with 
the  appearance  of  brush  discharge  potentials  fluctuated  enormously  at  once. 
When  the  machine  works  smoothly,  however,  the  disk  takes  a  stable  posi- 
tion for  a  sufficiently  large  D  and  may  then  be  brought  flush  with  the  surface 
(by  lowering  the  water  level)  without  difficulty.  Care  must  be  taken  to 
keep  the  centering  screws  above  the  water  level  {w  in  fig.  iib)  quite  dry. 
A  little  tapping  is  essential. 

In  all  the  above  experiments  3/  was  much  less  than  Z>,  so  that  the  disk 
rose  to  a  position  of  stable  equilibrium  below  the  point  at  which  continuous 
motion  from  the  bottom  to  the  top  plate  would  have  occurred.     Only  in 


46 


THE   DIFFUSION  OF  GASES  THROUGH 


the  last  case  of  the  second  series  for  the  case  of  the  metal  tube  was  the  limit 
of  stable  equilibrium  approached.  When  the  potential  is  unsteady  it  is 
necessary  to  keep  the  disk  some  distance  below  this.  For  the  case  of  the 
large  values  of  V  the  guard  ring  should  have  been  larger,  but  the  results 
as  a  whole  betray  no  discrepancy  attributable  to  this  effect.  To  detect  it, 
facilities  for  constant  potentials  of  the  degree  stated  would  have  to  be 
available.  In  conclusion,  the  simplicity  of  the  apparatus  as  a  whole 
deserves  remark. 


Table  ii. — Measurements  of  potential,  F'  =  2.26XioVg  ir^/R'^)lD^;  p=  i;2r  =  o.854cm. 
2i?  =  6.65  cm.     Al  tube  30  cm.  long;  weight,  13  grams. 


/ 

D 

io-»F 

[ 

D 

lO-'F 

f  ° 

55 

3.81 

17.2       0 

62 

3.81 

18.2 

I.  Apparatus,  figure  1 1  a < 

56 
72 

3 
3 

81 
56 

•7 
18 

3 
3 

79 
82 

3.81 
4.05 

20.5 
22.2 

l 

90 

3 

56 

20 

5 

72 

4.05 

20.8 

II.  Apparatus,  figure  1 1  b 1 

Metal  tube.                1 

47 
49 
165 

5 
5 
6 

08 
08 
35 

21 
21 
'5 

I 

6        I 

6 

44 
06 

5.08 
3.81 

20.4 
23.8 

f 

22 

4 

83 

13 

7 

42 

4.06 

15.9 

24 

4 

83 

>4 

3 

31 

5.08 

17. 1 

35 

4 

57 

16 

4 

38 

5-33 

20.0 

34 

4 

32 

15 

3 

43 

5-59 

22.2 

48 

4 

06 

17 

0 

38 

5-59 

20.9 

46 

3 

81 

15 

6 

48 

5.84 

24.5 

III.  Apparatus,  figure  n  b 

Glass  tube. 

67 
58 

3 
3 

56 
30 

•7 
'5 

6 

2 

53 
40 

6.10 
6.60 

26.9 
25.3 
23.6 

62 

3 

30 

>5 

7 

30 

7. II 

32 

5 

08 

17 

4 

27 

7.62 

24.0 

40 

5 

08 

19 

4 

22 

8.13 

23.1 

38 

4 

83 

18 

0 

16 

8.64 

20.9 

42 

4 

83 

18 

9 

16 

9.14 

22. 1 

38 

4 

57 

«7 

0 

10 

10. 16 

19.4 

^ 

44 

4 

32 

•7 

3 

IV.  Apparatus,  figure  1 1  b.     Glass  1 
tube.     Large  electrical  machine.  1 

70 

59 
42 

6 

7 
8 

35 
62 

89 

32 
35 
34 

I 

4 
8 

40 
1 1 
'9 

8.89 
10. 16 
10. 16 

34.0 
20.4 
26.8 

Part  II.    AbsoIvUTE  KlEctrometry  by  Aid  of  the  Cartesian  Diver. 

32.  Introductory. — In  the  above  methods  the  stem  between  the  floats 
and  the  movable  disk  of  the  condenser  passed  through  the  surface  of  the 
liquid.  This  introduces  capillary  forces  which  are  annoying  and  liable  to 
be  of  serious  magnitude.  To  obtain  the  utmost  sensitiveness  available, 
the  stem  must  be  discarded  and  the  movable  disk  in  question  mounted  on  a 
Cartesian  diver — the  whole  apparatus,  i.  e.,  both  plates  of  the  condenser 
and  accessories,  being  submerged  in  a  non-conducting  clear  paraffin  oil. 
The  remarkable  delicacy  in  weighing,  instanced  in  the  above  experiments  on 
the  diffusion  of  gases,  contributes  to  the  success  of  the  present  experim^ents. 


I.IQUIDS  AND  ALIylED  EXPERIMENTS. 


47 


33.  Apparatus. — The  construction  of  the  apparatus  is  shown  in  fig.  15 
in  vertical  section.  Here  ff'f'f  is  an  inverted  bell  jar,  with  a  ground  edge  at 
ff  and  a  neck  for  a  stopper  at  /'/'.  This  is  closed  with  a  brass  lid,  ee,  and 
contains  the  charge  of  paraffin  oil  as  far  as  the  level  ww.  The  plates  of  the 
condenser  are  shown  at  gg  and  hssh,  hh  being  the  guard  ring  and  55  the 
movable  disk.  In  order  that  hssh  may  be  nearly  plane  the  inner  circular 
edge  of  hh  is  turned  as  thin  as  possible  (not  shown).  The  plate  gg  is  held 
by  a  rod  aa  (with  a  clamp  screw  on  top),  the  latter  fitting  snugly  into  the 
hard-rubber  cylinder,  to  which  it  may  be  fastened  with  a  set  screw.  The 
cylinder  hb  is  in  turn  held  by  a  sleeve  and  set 
screw,  axially  and  vertically  at  the  center  of 
the  lid  ee.  Hence  gg  may  be  adjustably  raised 
by  any  desirable  amount,  or  lowered  into 
contact  with  hh. 

In  another  form  of  the  apparatus  the  rod 
aa,  holding  the  disk,  may  be  replaced  by  a 
micrometer  screw  and  stuffing  box. 

The  disk,  ss,  is  floated  on  the  Cartesian 
diver  k  of  very  thin  brass  tubing,  to  which  it 
is  soldered.  The  level  of  the  liquid  within 
is  shown  at  v.  Four  adjustable  bent  wires  // 
keep  the  float  in  position,  concentric  with 
the  axis  of  the  circular  plates  of  the  condenser, 
and  also  prevent  its  falling  below  a  conve- 
nient level. 

The  guard  ring  hh  is  supported  by  four 
strips  of  copper  nn  snugly  fitting  the  inside 
of  the  bell  jar.  These  are  braced  by  a  ring 
of  metal  mm,  to  which  the  strips  nn  are  sol- 
dered. They  terminate  at  the  top  of  the 
tube  pp,  which  is  the  lower  electrode  of  the 
condenser,  the  clamp  being  at  r.  The  tube 
pp  finally  is  held  in  place  by  the  perforated 
cork  qq,  all  parts  fitting  tightly.  In  a  fur- 
ther improvement  of  this  apparatus,  the  guard  ring  is  adjustable,  being 
placed  on  three  leveling  screws,  respectively,  rotating  with  three  springs. 
The  wires  //  are  also  adjustable. 

The  lid,  finally,  is  provided  with  the  tubulure  c  in  connection  with  the 
exhaust  pump  and  a  stop-cock  d  for  the  introduction  of  air,  the  tube  p 
below  being  closed  by  a  cock  (not  shown)  when  the  apparatus  is  used. 

The  apparatus  as  a  whole  is  held  in  a  suitable  standard,  and  the  ground 
edge  of  the  lid  ee  is  clamped  securely  (air-tight)  to  the  ground  top  of  Jf. 
All  other  joints  are  made  air-tight  by  an  appropriate  cement,  applied  on 
the  outside. 

To  adjust  the  apparatus  it  is  first  filled  with  oil,  through  pp,  to  the 
required  level,  the  bell  jar  being  placed  neck  upward  for  the  purpose  and 


Fig.  1 5. — Absolute  electrometer 
with  disk  carried  on  Cartesian 
diver. 


48  THB   DIFI^USION  OB*  GASES  THROUGH 

c  being  closed.  The  jar  is  then  inverted  as  in  the  figure,  pp  being  closed. 
Air  is  now  introduced  through  pp  in  small  bubbles,  which  are  caught 
within  the  Cartesian  diver  k,  until  the  requisite  amount  of  air  is  conveyed. 
During  this  operation  it  is  expedient  to  connect  the  air  pump  at  c  (d  being 
closed  throughout)  and  to  exhaust  the  air  above  w  to  the  identical  partial 
pressure  subsequently  to  be  used  in  the  experiment.  Air  is  then  allowed  to 
enter  k  through  p,  until  the  diver  just  floats.  On  closing  p  and  restoring 
atmospheric  pressure  through  k  the  diver  will  sink  as  far  as  its  supports. 

Clearly  the  diver  will  be  in  equilibrium  at  a  higher  artificial  presstue  in 
the  air  above  ww  when  the  condenser  is  charged  than  when  it  is  uncharged, 
because  of  the  attraction  of  electrical  forces.  This  difference  of  pressure 
is  the  basis  of  the  measurements. 

In  the  course  of  the  experiments  it  was  found  that  means  had  to  be 
provided  to  seciure  parallelism  between  the  disks  hh  and  gg  of  the  condenser. 
This  was  done  satisfactorily  by  placing  hh  on  three  suitable  set  screws, 
held  at  mm,  together  with  three  corresponding  downward- tending  springs. 
In  such  a  case  the  disk  hh,  in  the  absence  of  the  lid  ee  and  the  disk  gg,  may 
also  be  removed  on  loosening  the  springs,  an  operation  frequently  necessary, 
as,  for  instance,  for  the  insertion  of  different  divers  k.  The  supports  /  are 
to  be  adjustable  for  this  purpose. 

In  constructing  the  instrument  for  definite  purposes  a  metal  vessel  ffff 
should  be  used,  provided  with  opposed  plate-glass  windows,  through  which 
the  disk  hh  and  the  upper  part  of  the  diver  may  be  seen  during  measurement 
in  order  that  the  time  of  drop  may  be  ascertained.  The  disk  hh  would 
then  be  practically  a  horizontal  partition  in  the  vessel,  though  the  disks 
should  still  be  adjustable  for  parallelism.  The  pipe  pp  is  to  be  soldered  to 
the  bottom  for  efflux  of  oil  and  influx  of  air.  The  form  of  apparatus  given 
in  fig.  15,  however,  sufficed  very  well  for  experimental  purposes. 

Since  the  guard  ring  and  diver,  the  vessel,  and  lid  are  all  put  to  earth, 
while  the  movable  disk  gg  is  charged,  convection  may  be  produced  in  the 
oil  between  the  plates  in  case  of  high  potential.  Such  a  reaction  on  the 
disk  of  the  diver  may  tend  to  modify  the  equilibrium  and  the  amount  of 
such  an  error  will  have  to  be  shown  by  experiment;  but  nothing  serious  of 
the  kind  was  detected.  If  a  solid  plate  of  mica  or  glass  is  in,terposed  a 
variety  of  complications  enter,  which  will  be  referred  to  below. 

34.  Equations. — If  we  return  to  equation  (i).  Chapter  I,  and  neglect  m/M, 
the  ratio  of  the  mass  of  the  air  contained  in  the  Cartesian  diver  and  the 
weight  of  the  solid  vessel  (here  of  brass),  in  comparison  with  I, 

Pu>  Mg     I-Pjpg 

where  h  is  the  difference  between  the  level  of  the  liquid  within  the  diver 
and  in  the  bell  jar  {vw,  fig.  15),  H  the  corrected  pressure  in  centimeters  of 
mercmy  of  the  artificial  atmosphere  above  w,  p„,  p„,  Pg,  the  densities  of 
mercury,  of  the  liquid  floating  the  diver,  and  of  the  solid  walls  of  the  diver, 


LIQUIDS  AND  AI,I.IED  EXPERIMENTS. 


49 


respectively,  t  the  absolute  temperature,  R  the  gas  constant  for  air,  and  g 
the  acceleration  of  gravity.  This  equation  applies  when  the  uncharged 
diver  is  just  about  to  sink,  or  is  instantaneously  in  unstable  equilibrium. 

If,  now,  other  things  remaining  the  same,  the  diver  is  charged  to  potential 
V,  and  D  is  the  distance  apart  of  the  plates  of  the  condenser,  A  the  area  of 
the  movable  disk,  and  /  the  electric  pressure, 


F  =  30oDV87r/ 


(2) 


where  V  is  given  in  volts. 

The  effect  of  the  charge  is  to  keep  the  diver  suspended,  i.  e.,  to  virtually 
reduce  the  weight  Mg  hyJA .  More  water  will  have  to  enter  to  just  float  it. 
Hence  //  must  be  increased  to  H',  while  h  changes  slightly.     Hence 


h'-hir  - 


Rmr 


Pg       {Mg-fA)ii-pJpg) 

It  follows  from  equations  (i)  and  (3)  that 

Mg  {k'-h)p,,+  ar-H)p^ 
^      A  h'p^-\-H'p„ 


(3) 


(4) 


As  a  rule  h'  —  h,  which  refers  only  to  the  difference  of  level  of  the  liquid  in 
the  diver,  in  the  charged  and  uncharged  states,  may  be  neglected,  and  if  R 
is  the  radius  of  the  disk,  A  =  wR^,  so  that 


/= 


Mg      H'-H 


tR'  H'+hpJp^ 
If  this  be  substituted  in  equation  (2)  the  result  is  finally 


=  30of  J 


?,Mg 


H'-H 
H'+hpJp, 


(5) 


(6) 


It  is  interesting  to  obtain  an  estimate  of  the  numerical  value  oi  H'  —  H  for 
a  diver  which,  when  charged,  floats  at  about  atmospheric  pressure.  In  the 
apparatus,  fig.  1 5,  Jf  is  about  35  grams  and  R  about  3.5  centimeters.     Hence 


Zr'-Zr  =  3.8Xio"'F7Z) 


(7) 


and  roughly  the  data  given  in  table  1 2  apply,  the  numbers  not  defined  being 
H'  —  H  in  centimeters. 

Table  12. 


F=io 

F=ioo 

F=iooo 

F=ioooo 

r>=o.oi  cm. 
D=o.i  cm . 
D  =  I  cm . . . 

4Xio-« 

4 
4X10-* 

4 
4X10-* 

4 

50  the;  diffusion  of  casks  through 

With  the  disks  of  the  condenser  i  mm.  apart,  it  should  therefore  be 
possible  to  measure  50  volts,  the  difference  of  manometer  pressure  resulting 
being  about  o.i  mm.  of  mercmy.  From  this  limit  the  manometer  head 
rises  rapidly  as  the  square  of  V  or  inversely  as  the  square  of  D.  Thus  for 
50,000  volts  and  D=i  centimeter,  H'  —  H=  100  centimeters.  Hence  if  meas- 
m^ements  are  to  be  made  with  the  air  pump,  i.  e.,  with  H'  —  H  less  than 
the  equivalent  of  one  atmosphere,  D  will  have  to  be  increased  to  D  =  2  cm., 
where  H'  —  H  =25  cm.,  etc. 

Practically  the  determination  of  V  will  depend  upon  the  measurement 
H'  —  H  or  of  D.  The  latter  seems  to  be  the  more  convenient  datum, 
though  it  requires  a  screw  with  graduated  head  and  a  stuffing  box  in  place 
of  the  rod  aa  in  fig.  15,  i.  e.,  a  screw  micrometer  for  D.  In  such  a  case  let 
H'  —  H=  36  cm.,  a  convenient  mean  value.  In  other  words,  the  uncharged 
diver  is  to  just  float  when  the  artificial  atmosphere  is  about  36  cm.  below 
the  normal  barometer,  whereas  the  charged  rider  floats  for  different  values 
of  D.     Hence  by  equation  (7)  for  this  typical  case, 

F  =  3X10*1?  volts,  roughly 
or  numerically 

D  =  o.oi        o.i         i.o  2.0  cm. 

F  =  3oo         3,000    30,000    60,000  volts. 

In  other  words,  the  electrometer,  beginning  with  one  electrostatic  unit,  will 
be  suitable  for  measuring  the  ordinary  sparking  potentials  in  air  of  electro- 
static and  similar  machines;  for  the  distance  apart  of  the  plates  of  the 
submerged  condenser  would  probably  suffice  to  prevent  sparking  within. 
Moreover,  H'  —  H  is  large  enough  for  accurate  measurement. 

35.  Measurements. — For  convenience  the  following  experiments  are  made 
in  terms  of  H  —  H'  the  difference  of  manometer  pressures.  The  poten- 
tials used  were  produced  by  a  small  Wimshurst  machine,  eventually  kept 
in  rotation  by  a  small  motor.  The  data  are  given  in  table  13,  part  I. 
Different  values  of  H  were  used,  as  the  apparatus  was  not  quite  tight  below 
the  rider,  so  that  small  accessions  of  air  entered.  The  variations  of  V  are 
probably  due  to  the  electrical  machine,  which  was  here  turned  by  hand. 
The  table  shows  a  consistent  series  of  relative  values  for  V,  notwithstanding 
the  large  variation  given  to  D. 

The  diver  was  now  modified  by  soldering  it  to  a  small  sinker  below  in 
order  to  secure  greater  stability  of  vertical  flotation.  The  results  in  table 
13,  part  II,  show  considerable  improvement  and  there  was  no  leakage. 
Changes  of  V  are  again  probably  due  to  the  electrical  machine. 

Another  diver  was  now  inserted  having  a  breadth  of  tube  somewhat 
larger  than  the  above,  being  5  cm.  in  diameter  and  6  cm.  long.  Its  mass 
was  31.98  grams,  but  unfortunately  it  proved  to  be  slightly  top-heavy  in  the 
lighter  oil,  so  that  only  a  few  measurements  were  taken  (table  13,  part  III). 

The  addition  of  a  sinker  increased  the  weight  of  the  diver  to  37.89  grams, 
the  other  constants  being  the  same.     The  experiment  was  satisfactory 


LIQUIDS  AND  ALLIED  EXPERIMENTS. 


51 


throughout,  the  suddenness  with  which  the  charged  diver  breaks  off  being 
specially  marked.  Care  must  be  taken  to  decrease  pressure  slowly  in  order 
to  avoid  thermal  discrepancies.  Table  13,  part  IV,  is  an  example  of  the 
data  obtained. 

Table  13. — ^Measurement  of  potential. 


I. — Af=35  grams.  Disk,  3.5  cm.  in  di- 
ameter. Kerosene  oil,p=o.799  at  24°. 
Barometer,  76.14  at  17°.  Diameter 
of  diver  tube,  3.85  cm. ;  length,  8.8  cm. 


III. — M= 3 1. 98  grams.  Diameter,  2i?  = 
5.0  cm.;  length,  6  cm.;  slightly  top- 
heavy. 


D 

H' 

H-H' 

IO-3F 

D 

H' 

H-H' 

lo-^F 

cm. 

cm. 

cm. 

volts. 

cm. 

cm. 

cm. 

volts. 

0.32 

57-9 

9-5 

5.90 

1.27 

59-75 

9-53 

22.0 

•5' 

51.6 

3.2 

5.73 

1.27 

62.20 

10.45 

22.9 

.63 

50.3 

2. 1 

5.81 

1.27 

60.72 

8.80 

22.0 

.63 

52.. 

3.7 

7-75 

1.27 

61.62 

9.42 

21.7 

.63 

53.2 

5.0 

8.72 

1.27 

48.0 

.5 

5.81 

II. — M=35.795  grams.  Barometer,  75.70 
at  19°.  Diameter  of  diver  tube,  3.85 
cm.;  length,  8.8  cm.     Apu,/Pw»=o.3. 


IV. — M=  37.89  grams.    Diameter,  2R  ■■ 
5.0  cm.;  length  6  cm. 


D 

H' 

H-H' 

lo-'F 

D 

H' 

H-H' 

io-»7 

cm. 

cm. 

cm. 

volts. 

cm. 

cm. 

cm. 

volts. 

1.016 

38.48 

0.44 

5.6 

1.27 

58.08 

6.49 

20.2 

i.oi6 

52.91 

■97 

7." 

1.27 

59.83 

6.88 

20.4 

1.270 

37- '9 

1.05 

9.8 

1.27 
1.27 
1.02 

«.53 
1.79 
2.04 

60.51 
61.04 
68.43 
60. 12 

57.85 
57.81 

6.95 

7.08 

14.15 

5.70 

3-33 
3.05 

20.4 

20.5 

22.0 

22.3 

20.3 

22.  I 

These  values  of  V  for  so  large  variation  of  D  {H—H'  increasing  about 
5  times)  are  to  be  regarded  as  a  satisfactory  test,  the  fluctuation  of  values 
being  again  attributable  to  the  electrical  machine .  In  these  absolute  values , 
however,  the  potentials  V  found  were  somewhat  larger  than  would  follow 
from  the  results  of  an  interposed  spark-gap  with  balls  about  2  cm.  in  diam- 
eter. The  spark  would  have  been  equivalent  to  about  16,000  volts. 
Sparks,  however,  here  occur  too  rapidly  for  measurement. 

A  number  of  experiments  tried  by  interposing  solid  disks  between  the 
condenser  plates  led  throughout  to  inadmissible  results.  In  case  of  a  mica 
plate  lying  on  the  guard  ring,  the  whole  cylinder  of  oil  between  the  metal 
disk  at  the  top  and  the  mica  plate  must  eventually  have  reached  constant 
potential,  the  charge  being  carried  by  convection  to  the  top  face  of  the  mica. 
The  diver,  therefore,  clings  to  the  mica  plate,  which  in  an  insulating  medium 
can  not  be  again  discharged.  All  measurement  is  thus  out  of  the  question. 
In  case  of  thick  glass  plates  completely  filling  the  condenser  space,  other 


52 


THE   DIFFUSION  OF  GASES  THROUGH 


difficulties  were  encountered  from  the  frequent  presence  of  air  bubbles 
between  the  plate  and  the  disk  of  the  diver.  It  was  difficult  to  remove 
them  completely,  and  all  attempt  at  measurement  failed.  In  general  solids 
take  a  permanent  charge  which  can  not  be  removed  by  any  means  offered 
by  the  apparatus.  They  must  therefore  be  avoided  for  condenser  purposes. 
A  return  to  the  oil-condenser  with  a  number  of  minor  improvements 
showed  the  results  recorded  in  table  14. 

Table  14. — Constants  as  in  table  13,  III.     M= 37.89  grams. 


D 

H' 

H-H' 

lO-'F 

Spark. 

io-»F 

D 

H' 

H-H' 

lO-'F 

Spark. 

io-»F 

cm. 

cm. 

cm. 

volts. 

COT. 

volts. 

cm. 

cm. 

cm. 

volts. 

cm. 

veils. 

1.27 

51.66 

5   13 

19.0 

0.54 

19.0 

2.29 

50.83 

1.66 

19.5 

1.27 

52.00 

4.26 

17 

2 

2.04 

51.12 

1.90 

19.4 

0 

52 

18 

0 

1.27 

51.66 

3«4 

14 

b 

1.79 

51-35 

2.05 

>7-5 

1-53 

50.92 

2.13 

'4 

9 

47 

16 

0 

••53 

52.00 

2.63 

'7-5 

1.79 

50.23 

1.23 

>3 

2 

1.27 

53-77 

4-35 

17. 1 

47 

lb 

0 

2.04 

51.05 

2.05 

18 

8 

57 

'9 

0 

1.02 

57.20 

7-73 

17.7 

2.29 

50.70 

1.70 

«9 

8 

.76 

67.90 

18.48 

18.9 

2.55 

50.55 

1-45 

20.5 

1 

These  data  appear  to  be  trustworthy  throughout  and  measure  the  un- 
avoidable fluctuation  of  the  potential  of  the  electrical  machine.  They  are 
of  the  same  order,  moreover,  as  the  spark  potentials,  remembering  that 
these  had  to  be  determined  before  and  after  the  electrometer  potentials. 
Adequate  precautions  for  the  spark  work  could  not  be  taken.  The  range 
of  D  is  large,  increasing  from  0.8  cm.  for  the  largest  admissible  forces  to 
2.5  cm.  Below  0.8  cm^.  pressure  would  have  been  needed  to  sink  the  diver. 
In  case  of  table  14  the  diver  is  released  suddenly  and  falls  as  a  whole,  giving 
all  necessary  accuracy  to  its  H'.  Naturally  this  sudden  drop  is  essential, 
for  the  equations  used  are  only  true  when  the  disk  is  flush  with  the  guard 
ring.  A  diver  descending  obliquely  or  sluggishly  would  not  be  trustworthy. 
The  apparatus  need  not  be  air-tight  and  a  slight  leak  assists  in  the  determi- 
nation of  H'.  Other  similar  experiments  were  made  with  the  same  order 
of  values,  which  need  not  therefore  be  recorded  here. 

Finally,  certain  experiments  were  improvised  in  the  endeavor  to  measure 
relatively  low  potentials  of  the  order  of  300  volts.  Here  the  apparatus 
should  be  quite  free  from  leak,  as  the  change  of  H  under  these  conditions 
is  of  the  order  of  i  mm.  of  mercmy.  Any  thermal  discrepancy  in  the 
partially  exhausted  air,  the  presence  of  small  air  bubbles  clinging  to  the 
diver,  would  otherwise  mask  the  effect  to  be  measured.  Finally,  as  the 
distance  apart  of  the  plates  is  necessarily  small,  i  mm.  and  less,  special 
precautions  must  be  taken  with  this  magnitude.  The  results  obtained  need 
not  be  given  here,  as  the  work  was  undertaken  merely  to  show  that  the 
apparatus  works  smoothly  even  under  these  limiting  conditions. 

From  equation  (7)  above, 


AH=H-n'  = 


8Mg        isooyiy 


UQUIDS  AND  ALLIED  EXPERIMENTS.  53 

whence  it  appears  that  the  lightest  possible  diver,  observed  at  nearly  atmos- 
pheric pressure,  for  as  large  an  area  of  the  movable  disk  and  as  small  a 
distance  apart  of  the  condenser  plates  as  possible,  would  here  be  conducive 
to  the  best  results.     An  apparatus  constructed  so  that 

H'  =  75cm.  i2=i5cm.  D  =  0.05  cm.  M  =  60  grams 

should  show  AH=i  cm.  about  for  100  volts,  which  appears  to  be  the  lower 
limit  of  measurement.  The  higher  limit,  if  the  disks  are  made  small,  M 
and  D  large,  seems  to  be  indefinite,  providing  all  sharp  edges  can  be  obvi- 
ated. So  far  as  present  experiments  went  the  general  behavior  of  the 
apparatus  was  quite  satisfactory.  The  drop  is  rapid  and  definite,  facili- 
tating accurate  pressure  measurement.  The  apparatus  need  not  be  quite  air- 
tight, since  H'—H  is  the  variable  in  terms  of  which  potential  is  to  be  foimd. 
The  large  values  of  D  (several  centimeters)  which  seem  to  be  admissible 
without  vitiating  the  simple  form  of  equation  is  an  additional  advantage, 
so  that  sparks  may  in  a  measure  be  avoided.  A  heavier  oil  than  kerosene 
would  perhaps  be  advisable,  though  sparks  may  occur  without  danger  in 
any  case. 


CHAPTER  IV. 


THE  DIFFUSION  OF  GASES  THROUGH  SOLUTIONS  AND  OTHER  LIQUIDS. 

36.  Purpose. — In  the  earlier  investigation  (Chapters  I  and  II)  certain 
questions  were  left  outstanding.  The  first  of  these  refers  to  the  diameter 
of  the  column  of  liquid  through  which  diffusion  takes  place.  It  must  be 
decided,  if  possible,  whether  variations  in  the  area  of  the  column  exceeding 
its  minimum  area  have  as  small  an  effect  as  was  assumed.  Again,  when  a 
gas  other  than  air  is  examined,  the  Cartesian  diver  must  be  charged  in  an 
artificial  atmosphere  of  the  gas  in  question,  so  that  there  may  be  no  access 
of  air.  The  artificial  atmosphere  must  therefore  be  constantly  renewed. 
"Even  the  partial  exhaustions  should  be  made  so  far  as  possible  in  the 
absence  of  air.  Again,  endeavors  are  to  be  made  to  secure  adequately 
equable  temperature  conditions,  but  the  facilities  of  the  laboratory  for 
this  purpose  are  meager. 

Finally,  the  effect  of  the  solution  of  solids  and  liquids  on  the  rate  of 
diffusion  of  the  gas  through  water  is  an  interesting  question.  What  is  to 
be  determined  is  the  degree  to  which  the  physical  pores  of  the  pure  liquid 
are  stopped  up  with  different  quantities  and  different  kinds  of  solute. 
Different  solvents  may  also  be  taken  in  question. 

37.  Apparatus. — Hence  the  apparatus  with  which  the  present  experi- 
ments are  to  be  undertaken  must,  at  least  in  part, 
be  of  the  type  shown  in  fig.  4,  Chapter  II.  They 
were  constructed  in  some  variety,  but  the  form 
shown  in  the  annexed  fig.  16  was  finally  preferred. 
Here  vd  is  the  Cartesian  diver  capable  of  rising  in 
the  tube  cmm,  open  below,  closed  above  by  the 
stoppered  thermometer  t  and  kept  full  of  water. 
Thus  the  bulb  of  this  thermometer  serves  addi 
tionally  as  a  stop  for  the  diver  on  flotation.  The 
diver  must  fit  very  loosely  in  the  tube,  so  that 
there  may  be  a  minimum  of  viscous  resistance  to 
its  vertical  motion.  There  should  be  at  least  0.5 
cm.  clear  space  all  around  the  diver.  To  prevent 
it  from  sinking  completely,  a  vertical  sheet  of 
mica,  e,  slightly  flexed  so  as  to  hold  its  position  in 
an  axial  plane  by  reason  of  its  elasticity,  was 
eventually  adopted  in  preference  to  wire  gauze. 
The  wider  and  outer  tube,  ^4,  is  so  chosen  that  the  area  r  of  the  mouth  of 
the  diver  may  be  equal  to  that  of  the  annular  space  without,  as  nearly  as 
possible,  throughout.  The  gas  in  the  space  H  above  the  free  surface  /  of 
the  liquid  may  be  changed  and  kept  at  any  pressure  by  aid  of  the  tubes 
a  and  b. 

55 


Fig.  16. — Improved  Car- 
tesian diver  with  double 
tube  and  influx  pipe. 


56 


THE   DIFI^USION   OF  GASES  THROUGH 


The  tube  gg  is  of  use  in  charging  the  diver  with  gas.  For  this  purpose 
the  apparatus  A  is  inverted  and  then  brought  back  to  the  erect  position  in 
the  figure  so  that  the  diver  may  be  completely  filled  with  the  liquid.  The 
gas  in  question  is  then  introduced  in  small  bubbles  through  gg,  while  the 
gas  at  H  is  kept  about  at  the  pressure  (less  than  o.  i  atmosphere)  at  which 
the  experiment  is  to  begin.  WTien  the  diver  rises  the  tube  gg  is  closed.  It 
must  subsequently  be  quite  filled  with  the  liquid  by  suction  above,  so  that 
there  may  be  no  accidental  leakage  of  air  from  g  to  v.  In  fact,  the  tube  g 
may  with  advantage  be  straight.  Gas  may  be  led  into  v  by  tipping  the 
apparatus.     Otherwise  it  escapes  into  H  without  charging  the  diver. 

Table  15. 


No. 


M 


A.... 
B.... 
C... 
E.... 
F.... 
H. ... 
EE... 
FF... 
K,SO. 
BaClj 
A.... 
H... 


12.01 t 

37-425 
14.448 
14.897 

23 • 545 
11.653 
12.472 
10.939 
8.643 
7.496 
12.01 1 
11.653 


Pg 


Vessel. 


2.484 
2.470 
2.487 
2.466 
2.466 
2.466 
2.466 
2.466 
2.466 
2.466 
2.484 
2.466 


Tube. 


3  3 


45 


Float. 


6.8 
II. 3 
6.4 

7.1 


/ 

7 

7 

7 

7 

71 

6.8 

7  3 


7-8 

5-6 

6-7 
1 1-12 
11-12 

7-9 
J- 5-5 -5 

6-7 

6-7 

5-6 

7-8 

7-9 


When  relative  results  only  are  in  question,  as, for  instance,  when  different 
strengths  of  a  given  solution  are  compared  with  water,  the  simpler  appa- 
ratus with  a  single  tube  is  preferable.  It  is  virtually  standardized  with 
water  at  the  beginning  or  end  of  the  experiments.  Unfortunately,  in  the 
earlier  part  of  the  experiments  the  temperature  difficulty  was  still  encoun- 
tered in  the  following  work,  there  being  no  chamber  of  constant  temperature 
available.     Later  such  a  chamber  was  improvised. 

The  constants  of  the  floats  used  in  the  present  chapter  are  given  in 
table  15. 

The  divers  were  usually  cut  from  test  tubes  and  matched  with  regard  to 
the  area  of  their  mouths  with  the  area  of  the  stand  glasses,  in  order  to  make 
the  area  of  the  float  and  the  annular  area  outside  of  it  as  nearly  as  possible 
the  same.  The  tubes  should  be  of  relatively  heavy  glass,  so  as  to  insure  a 
low  position  of  the  free  surface  within,  permanently  in  the  cylindrical  part 
of  the  test-tube.  Otherwise  the  free  surface  is  liable  to  contract  into  the 
spherical  part  at  the  end,  and  a  correction  for  this  diminution  of  area  is 
difficult. 


LIQUIDS  AND  ALUED  EXPERIMENTS.  57 

38.  Equations.— It  will  be  expedient  in  the  present  research  to  compute 
the  coefficient  of  diffusion  by  volume,  relatively  to  standard  pressure  and 
temperature,  and  this  may  always  be  done  even  in  the  case  of  mixed  gases. 
The  flotation  experiments  thus  give 

70  \P„,  Pg/     r  \P^  Pg/    T 

where  Vq  is  the  volume  of  gas  in  cubic  centimeters  in  the  diver,  at  273° 
absolute,  and  76  cm.  of  the  barometer.  M  is  the  mass  of  the  swimmer, 
pg  its  density,  p„  the  density  of  the  liquid,  at  the  absolute  temperature  r. 
//  is  the  pressure  in  centimeters  of  mercury  at  which  flotation  just  takes 
place  at  the  given  fiducial  level.  If  B  is  the  barometric  height,  h  the  head 
(including  capillary  depression)  of  the  mercury  manometer  communicating 
with  the  gas  above  the  free  surface,  h'  the  height  of  the  bubble  of  gas  in 

the  swimmer,  tj     nih'     /         1  /n 

H  =  B-\-hpJp„-h-x-rr  (2) 

where  p„  is  the  density  of  mercury,  tt  the  vapor  pressure  of  water  or  of  a 
solution  at  r°,  x  the  surface  depression  of  the  cistern  of  the  manometer. 
In  all  the  adjustments  used 

//  =  jB+0.05  —  i.oih  —  T 
The  density  p^  is  easily  found  for  any  solution,  but  it  is  not  always  possible 
to  obtain  t'  the  reduced  vapor  pressure  due  to  solution.     Methods  will  be 
given  for  each  table.     Their  effect  is  usually  insignificant. 

The  above  equations  for  the  interdiffusion  of  two  gases  (//  initially  alone 
within  the  diver  and  finite  in  quantity,  A  without  and  unlimited  in  quan- 
tity) are,  as  above  shown,  when  the  volume  coefficient  k  refers  to  0°  C.  and 
76  cm.  of  mercury, 

2h"'-\-h" ' 

a '"" "  ^"^'^'^  ~  '^"^  '^"'^  ^"^*"^  ^^^ 

where  h"  and  h'"  are  the  heads  of  the  liquid  shown  in  fig.  16,  a  the  area  of 
the  diffusion  column,  p^  and  p^  the  partial  pressures  of  the  gases  within 
the  diver,  Kf^  and  «„  their  volume  diffusion  coefficients,  and  p„  the  density  of 
the  liquid.     Throughout  the  experiments  if  B  is  the  height  of  the  barometer 

B-r=^p^+P,-h"p„g  (4) 

Hence  if  but  a  single  gas  A  is  present,  p^  is  zero  and 

-i2h'''+h")Vo/a  =  K,h"p„g  (5) 

from  which  k^  may  be  computed  from  observations  of  v^  in  the  lapse  of 
time.     Moreover,  ,  ,  . 

KPQ=k  (6) 

the  coefficient  of  diffusion  referring  to  mass,  which  can  not  therefore  be  found 
except  in  case  of  a  single  gas,  where  po  is  given.     One  may  observe  that 

Vo/a  =  ho  (7) 

where  P  is  the  height  of  the  cylindrical  air  bubble  within  the  diver  at 
standard  pressure  and  temperature.  The  variations  of  h^  in  the  lapse  of 
time  are  not,  however,  measurable  with  adequate  accuracy. 


58  THE   DIFFUSION   OF  GASES  THROUGH 

In  equation  (3)  Kj,  can  not  be  found  even  when  k„  is  given,  unless  p^  is 
also  given,  which  is  not  generally  the  case  in  a  phenomenon  so  complicated. 
If  equation  (3)  is  expressed  in  terms  of  p^ 

Hence,  since  at  the  beginning  pa  =  ^, 

-{2h"'^-li"yoJa={B-ir+h"p,,g)K^-{B-T)K,  (9) 

so  that  for  given  k„,  k^  may  be  found  from  the  slope  of  the  initial  tangent  of 
the  time  graph. 

oh"'-i-h" . 
-         2      ^o=(B-T)K,-{B-^-h"p,g)K,  (10) 

so  that  Kj,  can  again  be  found  if  this  stage  of  diffusion  can  be  recognized, 
which  is  not  generally  the  case.     When  i'o  =  o, 

which  still  contains  the  two  unknown  quantities,  Pj,  and  /c,,,  for  known  k„. 

If  the  gases  within  and  without  the  diver  are  initially  identical,  but  in 
multiple  as  in  the  case  of  air,  the  quantities  being  limited  within  and  un- 
limited without, 

a '''o  =  ''a(.Pa-pa)+'<?>(P?,-p},)  i^V 

Since  B  —  Tr  =  p,^+paSindB  —  h"pf,,g  —  Tr  =  pf^  —  pa,the  equation  maybe  written 
2h"'-l.}i" .  , 

I'o  =  K  -  ^1)  Pa  -  i'<a  -  '^Z.)  Pa+^n  ^^" Pw  S  ( 1 3) 

If  Kg  and  Kj,  are  not  the  same,  the  term  involving  p^  is  variable  and  hence 
t'o  is  not  constant.  Theoretically  this  is  an  objection  against  the  use  of  air 
as  a  standard  gas.  In  practice,  however,  Vq  is,  apart  from  temperature 
discrepancies,  very  nearly  constant,  i.  e.,  the  departure  of  the  time  graph 
from  a  straight  line  throughout  a  sufficiently  long  interval  of  observation 
can  not  be  detected  (see  transpiration  figures.  Chapter  II).  Hence  the  two 
diffusion  coefficients  are  nearly  enough  the  same  to  justify  equation  (5)  in 
most  cases  if  sufficient  time  has  elapsed  to  establish  the  equilibrium  condi- 
tions. The  extreme  difficulty  of  using  any  other  gas  and  the  special  errors 
introduced  by  the  necessity  of  an  artificial  atm^osphere  more  than  counter- 
balance the  theoretical  preference  suggested. 

39.  Diffusion  of  Air  into  Air  Through  Water. — The  apparatus  used 
was  of  the  double-tube  type  of  fig.  16  and  its  dimensions  are  given  at  the 
head  of  table  16.  The  float  fitted  the  tube  somewhat  too  snugly,  so  that 
observation  was  ver>-  slow,  o^^ing  to  the  thin  sheet  of  water  between  diver 


LIQUIDS  AND  AIXIED   EXPfiRIMENTS. 


59 


and  tube.     Inasmuch  as  the  forces  are  known,  it  may  be  worth  while  to 

test  the  method  for  measuring  the  viscosity  of  the  liquid.     Table  16  and 

those  which  follow  contain  the  date,  the  corresponding  value  of  vo,  and  the 

other  data  needed  to  compute  k  by  equation  (5).     M  denotes  the  mass  of 

the  float,  Pg  its  density,  p„,  the  density  of  the  liquid  at  the  temperature  given. 

Diameters  of  vessels  are  referred  to  under  2r;  h',  h" ,  h'"  are  the  vertical 

heights  of  bubble,  the  water  head  for  the  diver  when  sunk,  and  the  effective 

height  of  the  water  level  within  the  diver,  above  its  mouth.     The  head  h" 

is  liable  to  vary  in  the  lapse  of  time. 

Table  16. — Air-air  through  water.  Vessel^  (double  tube).  J/=  12.011;  ^,=2.484; 
C=43.i4;  float,  2r=2.g^;  tube,  2r  =  3.3;  vessel,  2r=4.4.  h'=i.8,  ^"  =  4.7, 
h"'  =  7.o. 


Date. 

Barom- 
eter. 

/ 

H 

I'a 

Date. 

i _    __ 

Barom- 
eter. 

/ 

II 

t'o 

"C. 

! 
j 

"C. 

Sept. 17. . 

76.24 

20.7 

65.49 

5-775 

Oct.    12 

.     76.40 

22.6 

51 .21 

4.489 

18.. 

76.06 

21 .0 

65.80 

796 

'4 

.     76.88 

22.3 

49 

97 

4 

385 

19.. 

75.85 

21 .0 

65.26 

749 

15 

.      76.08 

22.4 

49 

43 

4 

336 

20. . 

76.03 

21.6 

64.86 

703 

16 

.     76.92 

'9  7 

47 

97 

4 

242 

21 . . 

76.90 

18.5 

63.65 

650 

'7 

76.44 

20.5 

47 

27 

4 

170 

23.. 

76.81 

17.0 

61.38 

474 

18 

.     76.38 

22.2 

47 

39 

4 

159 

24.. 

77.00 

17.0 

61.08 

447 

19 

•      75-97 

22.0 

46 

77 

4 

107 

25.. 

76.72 

'7-3 

60.60 

400 

21 

.      7729 

21.3 

45 

36 

3 

992 

26.. 

76.54 

>7-4 

60.34 

5 

375 

22 

.      77.08 

21 .2 

44 

83 

3 

946 

27.. 

76.31 

17.4 

59.70 

318 

!              ^^ 

.      76.05 

22.3 

44 

69 

3 

921 

28.. 

77.04 

19.0 

59.50 

5 

274  ; 

24 

.      75-29 

23.3 

44 

83 

3 

922 

30.. 

76.90 

17.2 

58.52 

216  I 

1              25 

•      75.68 

20.2 

43 

9' 

3 

877 

Oct.      1 .  . 

76.03 

17.7 

57-4' 

109 

26 

.      75.66 

20.0 

43 

36 

3 

831 

2. . 

76.58 

18.2 

57-05 

069 

i              ^« 

76.20 

20.0 

42 

39 

3 

745 

3-- 

76-33 

20.2 

56.74 

c 

010 

29 

.      76.58 

20.0 

4' 

94 

3 

706 

4- 

76.10 

23.0 

58. 20 

5 

095 

30 

.      75.80 

19.8 

4' 

42 

3 

662 

5-- 

76.69 

20.4 

56.68 

002 

Nov.    1 

•      75. 9' 

'9-4 

40 

61 

3 

595 

7- 

75.68 

19.0 

54  30 

4 

813 

2 

•      75-62 

19.4 

40 

42 

3 

578 

8.. 

76-34 

19.8 

53-43 

4 

724 

4 

•      77-33 

18.7 

39 

22 

3 

479 

9.. 

76.78 

21 .2 

52.87 

4 

654 

5 

4  76.89 

18.5 

39 

10 

3 

47' 

10. . 

76.27 

22.7 

52.64 

4 

611 

6 

.    76.82 

18.2 

38 

43 

3 

414 

II . . 

76.72 

21.6 

51.62 

4  539 

The  present  case  of  diffusion  of  air  through  water  in  the  double-tube 
apparatus  is  rather  a  disappointment  in  comparison  with  the  long  series  of 
results  obtained  above  wnth.  the  single-tube  apparatus,  inasmuch  as  the 
diffusion  after  all  allowances  are  made  for  differences  of  constants  takes 
place  much  faster  than  in  the  original  experiment.  Fig.  17,  moreover, 
apart  from  fluctuations  due  to  variation  of  solution  with  temperature, 
shows  two  different  rates,  the  slower  in  September  preceding  a  in  figure  and 
the  faster  in  October,  following  a,  v/hereas  no  variation  v*'hatever  had  taken 
place  in  the  apparatus  to  our  knowledge.  It  is  very  difficult  to  interpret 
this,  for  it  is  hardly  conceivable  that  any  appreciable  change  of  equivalent 
importance  should  have  occurred  in  the  air  of  the  room. 

The  excessive  rate  of  diffusion  here  observed  occurs  for  the  case  where 
the  diffusion  column  is  narrowed  throughout,  to  a  nearly  constant  diameter 
as  compared  with  the  large  diffusion  column  above  the  swimmer  which 


6o 


THE  DIFFUSION  OF  GASES  THROUGH 


obtained  in  the  earlier  experiments.  One  should  have  anticipated  a  slower 
rate  of  diffusion  if  any  change  of  rate  were  to  be  found.  The  reverse  is 
the  case. 

The  only  explanation  of  the  large  rate  encountered  may  possibly  be  found 
in  the  fact  that  the  partition  on  which  the  diver  descended  or  rested  during 
quiescence  was  a  sheet  of  clean  copper.  It  is  not  improbable  that  the  oxi- 
dation of  this  sheet  in  the  lapse  of  time  increases  the  effective  gradient  as 
the  metal  becomes  a  sink  for  oxygen.  In  other  words,  the  normal  diffusion 
gradient  is  enhanced  by  the  chemical  effect  introduced.  If  this  proves  to 
be  the  case,  the  experiment  presents  a  rather  sensitive  test  for  such  action, 
as  the  diffusion  coefficient  has  been  increased  nearly  three  times. 


5-6 

'\ 

\ 

54 

\ 

5S 

.. 

\ 

5^ 

^ 

,  a 

4-S 

•o 

\ 

V 

i 

4-fi 

S 
w 

\ 

1 

1 
j 

44 

.5i 

\ 

i 

4Z 

\ 

k 

1 

40 

\ 

m 

36 

1 

'\ 

cH 

"X^ 

^ 

^t 

16     Z 

1     :; 

iC^I 

« 

1 

« 

;     ;!i 

(     z 

6      S 

Ic/l'ov.i 

;     10 

Fig.  17. — Chart  showing  loss  of  standard  volumes  of  gas  in  diver 
in  lapse  of  days.     Diffusion  of  air  through  water. 

The  diffusion  coefficients  by  v^olume  k  computed  from  table  1 6  for  the  two 
rates  specified  are 

I'o  =  0.0445  c.c./day,  or  kXio^°=2.86      r^  =  0.0539  c.c./day       '^X  10*^  =  3.59 

showing  the  mean  value  10^^  =  3.22  ato^C.  and  76  cm.  of  mercury.  In 
view  of  these  discrepant  results  it  is  necessary  to  consider  the  case  of  air 
under  varying  conditions,  as  will  now  be  done  for  the  present  apparatus. 
In  §41,  moreover,  swimmers  of  different  dimensions  will  be  substituted. 

I  may  note  in  conclusion  that  a  gradually  rising  temperature  would 
decrease  the  apparent  diffusion  owing  to  the  gradual  rejection  of  gas  from 
the  water  within  the  diver,  whereas  a  gradually  falling  temperature  would 
have  a  reverse  effect.  It  would  be  very  difficult  to  discriminate,  in  such  a 
case,  between  the  true  diffusion  and  the  solution  discrepancy. 

The  double-tube  apparatus  A  was  eventually  removed  to  a  vault  of  more 
constant  temperature  and  taken  out  for  observation  only,  leaving  the 
copper  partition  in  place.     These  new  results  are  included  in  table  16,  after 


UQUIDS  AND  ALUED  EXPBRIMeNTS. 


6l 


October  24,  and  fig,  17,  following  b,  at  the  end  of  each.  The  new  dififusion 
constants  were  somewhat  smaller  than  the  above,  but  they  are  still  much 
higher  than  the  normal  values,  i.  c,  the  new  data  are  equivalent  to 

Wq  =  0.0383  c.c./day;  whence  io^''k  =  2.56 

To  interpret  this  result,  it  will  first  be  necessary  to  remove  the  copper 
partition,  which  has  been  supposed  to  be  an  absorbent  for  oxygen,  and  to 
replace  it  by  a  partition  of  mica.  This  will  be  done  in  the  next  paragraph. 
Including  the  last  results  the  mean  constants  for  the  50  days  of  obser- 
vation would  be 


1-0  =  0.0505  c.c./day 
retaining  the  abnormally  high  value. 


io*''k  =  3.38 


40.  The  Same,  Continued. — ^l^he  apparatus  was  now  taken  apart, 
the  copper  partition  removed  and  replaced  by  one  of  mica  of  the  same 
height.  It  was  then  charged  with  fresh  water,  etc.,  and  placed  in  the  vault 
in  question.     The  record  of  observations  is  given  in  table  17  and  fig.  18. 


Table  17. — Air-air  through  water 

Vessel  A  (double  tube] 

.     Copper  partition 

replaced  by  mica.     Constants 

as  in  table 

16. 

Date. 

Barom- 
eter. 

/ 

H 

t'o 

Date. 

Barom- 
eter. 

/ 

H 

fo 

Nov.    9. . 

75-55 

18.9 

67.63 

5.996 

Dec.     3 

•     76.45 

0 
16.5 

58.58 

5  233 

It . . 

76.33 

18 

9 

65.83 

837 

4 

.      76.30 

16 

7 

58 

52 

5.224 

12. . 

75.85 

18 

7 

65.22 

786 

5 

.     77.06 

>7 

0 

58 

5' 

5.219 

13.. 

76.17 

19 

0 

64-59 

725 

6 

•      75-75 

«7 

4 

58 

68 

5.227 

14.. 

75.69 

19 

0 

64.22 

692 

7 

.      76.14 

«7 

8 

58 

83 

5  234 

15.. 

75-72 

18 

7 

63.82 

661 

9 

.      76.28 

•7 

8 

59 

06 

5.254 

16.. 

76.52 

18 

5 

63.48 

635 

10 

•      76.33 

'7 

8 

58 

93 

5  243 

i8.. 

76.26 

18 

0 

62.49 

556 

II 

•      75-92 

'7 

6 

59 

05 

5253 

19.. 

76.29 

17 

7 

62. 10 

527 

12 

.      76.16 

'7 

7 

58 

85 

5-237 

20. . 

75.97 

>7 

5 

61 .70 

495 

»3 

.      77- 'o 

>7 

3 

58 

67 

5.228 

21. . 

76.31 

«7 

2 

61.39 

472 

>4 

•      76-74 

•7 

0 

58 

45 

5.214 

22. . 

75-94 

'7 

4 

61.18 

450 

16 

•      75-40 

'7 

3 

58 

24 

5.189 

23.. 

76.08 

>7 

5 

61.09 

441 

'7 

•      76-45 

•7 

4 

58 

26 

5.189 

25.. 

74  9« 

17 

3 

60.79 

4'7 

18 

.      76-40 

'7 

5 

57 

89 

5.156 

26.. 

76.20 

•7 

3 

60.60 

400 

>9 

■      74-34 

»7 

6 

58 

>7 

5   «79 

27.. 

76.38 

•7 

I 

60.44 

389 

20 

.      75.88 

'7 

4 

57 

93 

5. 160 

29.. 

76-95 

16 

6 

59-79 

340 

21 

•      76-57 

»7 

7 

57 

80 

5-144 

30.. 

76.79 

16 

6 

59.38 

303 

23 

•      76.75 

«7 

4     57 

30 

5.104 

Dec.    2 . . 

76.60 

16.6 

58.62  , 

5235 

M 

V 

<rS 

\ 

N 

Vf 

1 

V 

^^ 

M 

$•• 

"^ 

^ 

■-*-*, 

&« 

. 

"%. 

"^ 

c*Jw.  9      ^      P       Ti      29  ^e.4       9       U      49      2* 

Fig.  18. — Chart  showing  loss  of  standard  volumes  of  gas 
in  diver  in  lapse  of  days.  Diffusion  of  air  through  water. 


62 


THS   DlFlfUSIOX   OF   GASES  THROUGH 


It  Avill  be  seen  that  the  nevv  march  of  volumes  in  the  lapse  of  time  is 
essentially  curvilinear  throughout  the  whole  inter\''al  of  examination  of 
37  days.  Only  at  the  end,  abruptly,  a  nearly  constant  rate  appears  which 
is  abnormally  low.     The  initial  constants  are  roughly 

t;o  =  o.0225  c.c./day,  or  io^''k=i.43 

and  the  final  constants 

t>o  =  o.oo72  c.c./day,  or  10^^^  =  0.46 

Thus  the  mica  support  has  not  changed  the  erratic  behavior  in  the  flotation 
in  this  vessel,  in  which  the  constants  have  fallen  in  about  90  days  from 
io^''k  =  3.4,  an  enormously  high  value,  to  io^\'  =  o.46,  an  abnormally  Ioav 
value,  as  compared  with  the  usual  result  of  about  io^^K  =  o.g.  All  attempt 
to  interpret  this  exceptional  record  has  remained  futile,  but  it  induced  us 
to  discard  the  double-tube  apparatus  in  most  of  the  experiments  below,  as 
being  not  only  much  more  difficult  to  manipulate,  but  (for  some  occult 
reason)  liable  to  be  imtrustworthy  in  its  indications,  even  after  long  lapses 
of  time  within  which  equilibrium  conditions  would  certainly  have  appeared. 

41.  Diffusion  of  Air  into  Air  Through  Water;  Further  Experiments. — 

The  peculiar  behavior  of  air  in  the  diffusions 
of  §39  made  it  necessary  to  install  a  series 
of  further  experiments  in  which  the  dimen- 
sions of  the  swimmer  were 
suitably  varied.     The 
double-tube  apparatus  H, 
after  the  work  for  which 
it  was  destined  had  been 
completed,  w^as  also  ad- 
justed for  air  diffusion.     In  addi- 
tion to  this,  there  are  results  for 
the  diffusion  of  air  through  water 
to  be  made  in  connection  with 
each  of  the  vessels  in  which  air  is 
to  diffuse  through  solutions,  in 
50cMv.4      9      M'     ^      tt        order  that  suitable  standards  may 

Fig.  19.  A,  B,  c— Chart  showing  loss  of  stand-  i»  ^very  case  be  available. 

ard  volumes  of  gas  in  diver  m  lapse  of  days.       In  tables  1 8  and  19  two  similar 
Diffusion  of  air  through  water.  ^.^.^^.^    ^^^^^    introduced    into    a 

single-tube  apparatus.  They  were  both  made  exceptionally  long,  with  a  small 
head  h"  and  large  diffusion  column  h"-]r2h"',  the  swimmers  being  11  to  12 
cm.  in  length.  The  effect  of  this  would  naturally  be  to  increase  the  solution 
discrepancy.  One  diver  was  somewhat  heavier  than  the  other,  the  masses 
being  about  15  and  23.5  grams,  respectively.  Finding  that  the  diffusion 
progressed  with  exceptional  slowness  but  quite  identically  (see  figs.  19  a 
and  b)  in  character  in  the  two  vessels,  the  light  diver  was  now  cut  down  to 


SepmOdS 


LIQUroS  AND  AlrLIED  EXPERIMENTS. 


63 


a  length  of  but  4.5  to  5.5  cm.  and  the  experiment  continued  under  these 
conditions.  The  records  are  given  in  tables  18,  19,  20,  and  figs.  19  a,  b,  c, 
the  long  swimmers  showing  astonishingly  slow  diffusion.  Both  were  moved 
to  the  vault  of  constant  temperature  on  October  25.     (Cf.  c  in  fig.  19B). 


Tabls  19.- 

—Air-air  through  water.  Vessels  (single  tube).  1/= 23. 5450  grams; 

C=84.58; 

Pa 

=2.46^ 

;  float,  2r= 

=3.00  cm.;  vessel,  2r=4.7  cm. 

Date. 

i  Barom- 
1    eter. 

/ 

H 

Po 

Date. 

Barom- 
eter. 

/ 

H 

t'o 

Sept.  30 

.     76.90 

0 
«7-4 

65.77    •' 

428 

Oct.  21.. 

77.29 

0 
21.2 

65.64 

11. 271 

Oct.     I 

.     76.0^ 

18.0 

65.40    II 

342 

22. . 

77.08 

21.2 

65 -47 

11.242 

2 

.     76.58 

18.5 

65.45     >" 

333 

23.. 

76.05 

22.3 

65.86 

11.273 

3 

•     76.33 

20.4 

65.97     •! 

357 

24.. 

75  29 

23-5 

66.29 

11.304 

4 

.     76.10 

22.8 

66.77    H 

410 

25.. 

75.68 

20.3 

65.61 

11.299 

5 

.     76.60 

20.4 

66.26    II 

407 

26.. 

75.66 

20.2 

65.41 

11.266 

7 

.      75-68 

19.0 

65.67    u 

354 

28.. 

76.20 

20.2 

65.13 

n.2i8 

8 

•     76.34 

19.6 

65.70    II 

338 

29.. 

76.58 

20.0 

65.09 

11.219 

9 

.     76.78 

21 .2 

66.12    II 

353 

30.. 

75.80 

19.9 

65.06 

II. 217 

10 

.      76.32 

22.8 

66.52    II 

368 

Nov.  I .  . 

7591 

19-5 

64-91 

11.205 

II 

•      76.72 

21.7 

66.37    n 

379 

2.  . 

75.62 

19.5 

64.76 

1 1. 179 

12 

.     76.40 

22.7 

66.60    II 

384 

4-- 

77-33 

18.9 

64-45 

1 1. 147 

'4 

.      76.88 

22.5 

66.51     II 

376 

5-- 

76.89 

18.5 

64.36 

1 1. 144 

«5 

.     76.08 

22.4 

66.39    n 

359 

6.. 

76.82 

18.3 

64.27 

1 1. 136 

16 

.      76.92 

'9-7 

65.54    II 

306 

7,  . 

76.02 

•  8.3 

64.16 

II. 117 

17 

•      76.44 

20.5 

65.53    II 

277 

8. . 

75.07 

18.7 

64.26 

II. 119 

18 

.      76.38 

22.2 

66.04    II 

305 

9-- 

75-55 

18.9 

64.32 

11.124 

•9 

•      75-97 

22.1 

66.04    II 

309 

II. . 

76.33 

18.9 

64.25 

II. 112 

The  identity  of  the  two  curves,  figs.  19  a  and  B,in  their  indirect  fluctuation 
with  temperature  is  noteworthy,  showing  that  the  relative  results  obtained 
with  a  given  apparatus  are  quite  trustworthy.  The  new  feature  which  the 
curves  bring  out,  how^ever,  is  unexpected.  In  other  words,  the  rate  of 
diffusion,  which  was  incidentally  found  to  be  relatively  large  in  table  16, 
is  here  relatively  small,  only  about  one-tenth  of  the  former  value.  If  the 
mean  slope  of  the  curv^e,  fig.  19  a,  be  taken,  the  data  for  the  diffusion  con- 
stants are 

10  =  0.0042  c.c./day  or  io^*'k  =  0.374 
where  the  curve  of  fig.  19  b  for  the  same  interval  of  time  w'ould  have  given 
an  identical  result.     It  was  therefore  to  be  feared,  in  so  far  as  these  results 


64 


THE   DIFFUSION   OF  GASES  THROUGH 


are  inadmissible,  that  diffusion  decreases  with  the  length  of  column  at  a 
retarded  rate;  or  that  the  normal  volume  of  gas  diffusing  per  second 
through  a  column,  cat.  par.,  is  not  directly  dependent  upon  the  pressure 
gradient,  but  decreases  more  rapidly  than  the  gradient.  For  long,  slender 
swimmers,  /=ii  to  12  cm.,  k  is  so  much  reduced  as  to  suggest  that  for 
greater  lengths  of  column  it  would  practically  vanish.  Such  a  behavior 
was  quite  puzzling.  The  only  method  of  interpreting  it  seemed  to  consist 
in  continuing  the  observations  in  table  20,  while  the  diver  in  table  19  was 
cut  down  to  half  its  length  for  correlative  observation. 

The  apparatus  E,  after  the  long  swimmer  had  been  cut  down  to  the  small 
length,  showed  the  results  recorded  in  table  20  and  fig.  19  c. 

Tabus  20. — Air-air  through  water.    Vessel  E.    Small  swimmer.     il/=  12.4716  grams; 
^^=2.466;  C=44.8o;  float,  2r  =  3.oo  cm.;  vessel,  2r  =  4.7  cm. 


Date. 

Barom- 
eter. 

/ 

// 

Vo 

Date. 

1 

Barom- 
eter. 

/ 

11 

Vo 

Oct.   21 

•      7729 

0 
21 .2 

65.49 

5.956 

Nov.    8 

1 
•      75-07 

0 
23-5 

61.94 

5-595 

22 

.      7708 

21  .2 

64.65 

880 

9 

•      75 

55 

18 

7 

60.35 

^ 

532 

23 

.      76.05 

22.3 

64.79 

874 

1 1 

•      76 

33 

18 

7 

59-37 

5 

442 

24 

•      75  29 

23-5 

65.13 

883 

12 

•      75 

85 

18 

7 

59.04 

7 

411 

25 

.      75.68 

23.4 

65.  10 

882 

•3 

•      76 

»7 

18 

7 

58.74 

5 

384 

26 

.      7.S.66 

22.0 

64.65 

866 

'4 

•      75 

69 

18 

7 

58.61 

372 

28 

76 .  20 

21  .0 

63.66 

794 

15 

-      75 

72 

i8 

7 

58.36 

349 

29 

.      76.58 

19.9 

62.97 

75' 

16 

•!     76 

52 

18 

5 

58.20 

338 

30 

.      7580 

21  .2 

63.05 

735 

18 

■1     76 

26 

18 

0 

57-52 

284 

Nov.    1 

•      75-9" 

19.5 

62.05 

673 

'9 

•      76 

29 

•7 

7 

57.20 

260 

2 

■      75  62 

20.0 

62.20 

679 

20 

•      75 

97 

17 

5 

56.84 

230 

4 

•      77-33 

17.6 

60.44 

560 

21 

•      76 

31 

•7 

2 

56.61 

214 

5 

.      76.89 

20.2 

60.84 

551 

22 

■      75 

94 

•7 

4 

56.37 

188 

6 

.      76.82 

21.8 

61.32 

568 

23 

.      76.08 

•7 

4 

56.18 

171 

7 

76.02 

23.6 

61.88 

5^  587 

' 

A  line  drawn  through  the  observations  as  a  whole  is  equivalent  to  the 
following  rate : 

^0  =  0.0232  c.c./day  or  10^^  =  0.64 

This,  though  small,  is  a  closer  approach  to  the  normal  value  for  air  found 
in  Chapter  II.  The  result,  however,  might  nevertheless  give  credence  to 
the  occurrence  of  a  length  effect,  since  it  may  imply  that  diffusion  varies 
with  the  length  of  diver  and  column.  This  improbable  and  disconcerting 
eventuality  is  dispelled  by  the  final  data  of  table  19  for  the  long  diver  after 
the  time  interval  of  observation  had  been  adequately  increased.  It  follows, 
therefore,  that  these  long  divers  merely  accentuate  the  discrepancy  due  to 
the  thermal  changes  of  solution;  for  the  results  obtained  with  the  long 
swimmer  are  (fig.  19B) : 


z'o  =  0.0082  c.c./day  and  10^^  =  0.78 

which  agree  admirably  with  the  results  of  Chapter  II. 
The  length  effect  is  thus,  fortunately,  illusory. 


(See  table  21.) 


LIQUIDS  AND  ALLIED  EXPERIMENTS. 


65 


As  a  whole,  these  experiments  show  the  absolute  necessity  of  long  inter- 
vals of  observation.  Whether  it  be  a  gradual  decline  in  temperature  or 
solutional  effects,  or  whether  fresh  solutions  or  even  water  require  a  long 

Table  21. 


time-interval  to  reach  rigorously  normal  conditions  of  equilibrium,  the 
result  is  patent  that  the  true  diffusion  rates  do  not  appear  until  the  time- 
interval  has  been  prolonged  sometimes  as  much  as  five  or  six  weeks.     Even 


Table  22.- 

—Air-air  through  water. 

Vessel  H  (double  tube).     Constants  as  in 

table  33. 

Date. 

Barom- 
eter. 

/ 

// 

Vq 

Date. 

Barom- 
eter. 

t 

H 

I'O 

Oct.  26 

.      75-66 

0 
22.7 

66.19 

5  599 

Nov.  14 

1    75.69 

0 
19.5 

6\  .00 

5.211 

28 

■      76 

20 

21.8 

64.88 

504 

15 

•I     75-72 

19 

5 

60.79 

193 

29 

■      76 

58 

20.6 

64.15 

462 

16 

•      76.52 

19 

1 

60.57 

181 

30 

•      75 

80 

21.9 

64.17 

442 

18 

.      76.26 

18 

6 

59.81 

123 

Nov.    I 

■      75 

9< 

20.0 

63.15 

386 

«9 

.      76.29 

18 

3 

59-42 

095 

2 

•      75 

62 

20.7 

63.48 

403 

20 

•      75-97 

18 

1 

59-13 

073 

4 

•      77 

33 

.8.3 

61.78 

298 

i             21 

-      76-31 

'7 

9 

58.98 

064 

5 

•      76 

89 

20.8 

62.41 

3" 

1             22 

•      75.94 

18 

0 

58.79 

046 

6 

•:     76 

82 

22.4 

62.94 

329 

23 

.      76.08 

18 

1 

58.59 

027 

7 

•i     76 

02 

24.2 

63.78 

370 

;        25 

-      74  9" 

18 

0 

58.31 

005 

8 

•      75 

07 

24.0 

64. 12 

403 

1        26 

76.20 

18 

0 

58.11 

987 

9 

•      75 

55 

"9  3 

62.59 

351 

1        27 

.      76.38 

•7 

8 

57-72 

957 

1 1 

•      76 

33 

•9  5 

61 .50 

254 

29 

•      76.95 

17 

1 

56.80 

888 

12 

■      75 

85 

19  5 

61 .  15 

224 

30 

•      76-79 

'7 

5 

56.26 

837 

«3 

•      76- 17 

19.5 

61 .03 

5.214 

48 


V. 

Jk 

'V 

^\ 

V,. 

?>' 

*x 

N 

()ctS£     3/c^.5     iO      15      ZO     Z5     30 


Fig.  20. — Chart  showing  loss  of  standard 
volumes  of  gas  in  diver  in  lapse  of 
days.     Diffusion  of  air  through  water. 


if  the  curve  is  smooth,  it  is  always  hazardous  to  assume  that  the  true  diffu- 
sion rate  has  been  exhibited  within  a  month. 

The  double-tube  apparatus  //  charged  with  fresh  water  and  air  showed 
the  diffusions  contained  in  table  22  and  fig.  20. 


66  THH   DlFlfUSION  OF  GASES  THROUGH 

The  rate  of  diffusion  appears  as 

1)0  =  0.0185  c.c./day  or  10^^  =  0.90 


a  value  which  again  approaches  the  normal  result  in  Chapter  II,  and  affords 

strong  credence  that  the  much  more  troublesome  double-tube  apparatus  is 

unnecessary  in  practice. 

It  is  interesting  to  compare  figs.  19  c  and  20,  which,  though  obtained 

with  totally  different  apparatus,  show  identical  thermal  discrepancies. 

The  new  results  obtained 
with  apparatus  A  have  already 
been  discussed.  Table  21 
is  a  brief  summary  of  the 
values  for  the  diffusion  of  air 
through  water  as  obtained  from 
totally  different  apparatus  and 
charges.!  The  untrustworthy 
results  (vessel  ^4)  are  omitted. 


e4f 

\      .-**s 

fw 

M 

^ 

!»« 

) 

!H 

^Z 

l\ 

5rO 

\ 

4-S 

4« 

44 

^^* 

V 

42 

\ 

4^ 

V 

JW 

\ 

26  Ck/         6       11        16       Zi      26 

Fig.  2 1 . — Chart  showing  loss  of  standard  volumes 
of  gas  in  diver  in  lapse  of  days.  Diffusion 
of  hydrogen  through  water. 


42.  Diffusion  of  Hydrogen 
into  Hydrogen  Through 
Water. — The  apparatus 
(double  tube,  fig.  16)  and  ar- 
rangements of  results  in  table 
23  are  the  same  as  in  the  pre- 
ceding case  of  air.  In  the 
present  instance,  however,  an 
artificial  atmosphere  of  hydro- 
gen had  to  be  supplied.  This 
was  obtained  from  a  large  gas- 
ometer, a  slow  current  of  gas  from  the  same  passing  over  the  surface  of 
the  liquid  day  and  night.  The  gas  as  introduced  into  the  diver  through 
the  lateral  tube  in  fig.  16  was  necessarily  taken  from  the  same  gasometer, 
so  that  the  gases  within  and  without  the  diver  might  be  initially  identical. 
The  case  of  diffusion  of  hydrogen  through  water,  in  the  double-tube 
apparatus,  presents  at  the  outset  the  usual  meandering  irregularity,  here 
due  to  the  fact  that  the  measurements  were  at  first  made  in  a  temporary 
medium  of  air.  It  was  supposed,  in  view  of  the  brief  time  of  exposure, 
that  no  serious  discrepancy  would  be  introduced;  but  the  reverse  is  the 
case.  Consequently,  for  the  remainder  of  the  work,  beginning  about 
October  i,  the  observations  were  made  in  the  almost  entire  absence  of  air, 
the  artificial  atmosphere  of  hydrogen  being  kept  in  place  during  and  after 
the  partial  exhaustion  incident  to  measurement.  The  results  are  now  regu- 
lar, sho^ving  the  inevitable  variations  of  the  temperature  of  the  room  which 
from  the  low  solubility  of  hydrogen  are  insignificant  in  comparison  with  air. 


LIQUIDS  AND  AI^IvIBD  EXPERIMENTS. 


67 


The  diffusion  coefficients  of  hydrogen,  computed  from  table  23,  are 

»(,  =  o.o8o  c.c./day  or  10^^  =  3.4 

They  are  again  larger  than  found  in  Chapter  II ;  but  the  differences  are  such 
as  might  be  ascribed  to  differences  of  composition,  seeing  how  extremely 
sensitive  the  method  is  to  slight  impurities  in  the  diffusing  gas,  which  can 
not  be  kept  rigorously  pure.  There  remains  the  inherent  temperature 
effect,  the  influence  of  which  on  diffusion  proper  (apart  from  solution)  has 
yet  to  be  investigated,  both  for  hydrogen  and  for  air.  It  is  noteworthy, 
however,  that  the  k  of  the  present  observations,  i.  e.,  in  a  diffusion  column 

Table  23. — Hydrogen-hydrogen  through  water.  Vessel  H  (double  tube).  M=  1 1.653 
grams:  p^/  =  2.466;  C=4i.85;  float,  2r  =  3.05  cm.;  tube,  2r=3.4  cm.;  vessel, 
2r  =  4.6  cm. 


Date. 

Barom- 
eter. 

/ 

// 

Vo 

Date. 

Barom- 
eter. 

/ 

// 

To 

Sept.  17.. 

76.24 

0 
22.5 

7'-37 

6.041 

Oct.     7.. 

75.68 

0 
20.0 

61 .92 

5.281 

18.. 

76.06 

21.5 

6975 

5.922 

8.. 

76.34 

20.2 

61.10 

5 

208 

19.. 

7585 

22.0 

69.71 

5.910 

9.. 

76.78 

21.8 

60.30 

5 

n5 

20. . 

76.03 

23.0 

70.51 

5-959 

10.  . 

76.27 

23.0 

60.04 

5 

074 

21. . 

76.90 

19.6 

70.20 

5.995 

II.. 

76.72 

22.0 

58.88 

4 

992 

23.. 

76.81 

18.2 

70. 16 

6.017 

12.  . 

76.40 

22.9 

58.41 

4 

938 

24.. 

77.00 

18.2 

70.30 

6.029 

14.. 

76.88 

22.7 

56.42 

4 

772 

25.. 

76.72 

18.2 

70.22 

6.023 

"5    - 

76.08 

22.7 

5523 

4 

672 

26.. 

76.54 

18.4 

70.07 

6.006 

16.. 

76.92 

20.0 

53-57 

4 

569 

27. . 

76.31 

.8.4 

69.84 

5.986 

17.. 

76.44 

20.8 

52.59 

4 

475 

28. . 

77  04 

19.9 

69.73 

5  950 

18.. 

76.38 

22.4 

52.20 

4 

420 

30.. 

76.90 

18.0 

68.86 

5.910 

19.. 

75-97 

22. 1 

51-23 

4 

342 

Oct.      I . . 

76.03 

18.4 

67 -34 

5  772 

21 .  . 

77.29 

21 .4 

48.79 

4 

'44 

2. . 

76.58 

19.0 

66.67 

5-704 

22.  . 

77-08 

21.3 

47.42 

4 

029 

3- 

76 -33 

20.7 

66.01 

5.618 

23  •• 

76.05 

22.4 

46.54 

3 

941 

4-- 

76.10 

23.0 

65.78 

5.560 

24.. 

75.29 

23.5 

45.71 

3 

857 

5-- 

76.69 

21.0 

64.47 

5.482 

t 

nearly  constant  in  diameter,  comes  out  larger  than  it  was  found  above  for 
a  widening  column.  In  any  case  the  true  diffusion  coefficient  for  rigorously 
pure  hydrogen  is  yet  to  be  found,  inasmuch  as  the  small  admixtures  in 
question  have  so  marked  an  effect.  Thus  the  gas  in  the  gasometer  which 
is  used  for  the  artificial  atmosphere,  even  if  generated  quite  pure,  soon 
becomes  appreciably  less  so,  since  it  must  suffer  contamination  with  the  air 
diffusing  through  the  water  of  the  gasometer  over  which  the  hydrogen  is 
stored.  Since  such  large  quantities  are  needed,  mercury  storage  is  nearly 
out  of  the  question.  Hence  the  work  with  hydrogen  was  abandoned  tem- 
porarily at  this  stage,  the  coefficient  last  found,  io^*'/c  =  3.4  ^or  the  volume 
diffusion  at  o°C.  and  normal  pressure,  being  preferable. 

43.  Diffusion  of  Air  into  Air  Through  KCI  Solution. — ^The  solution  of 
KCl  contained,  after  mixing,  about  120  grams  in  600  c.c.  of  solution.  Its 
density  was  foimd  to  be  1.1133  at  24.5*'.  From  this  a  table  of  densities 
p^was  computed  between  16°  and  25°,  assuming  the  expansion  to  be  the 


68 


THE   DIFFUSION  OF  GASES  THROUGH 


same  as  that  of  water.  The  solution  may  therefore  be  regarded  as  holding 
20.8  grams  of  KCl  in  loo  grams  of  water,  or  17.2  grams  of  salt  in  100  grams 
of  solution.  To  obtain  the  vapor  pressure  tt'  of  the  moist  air  above  the 
solution,  it  was  at  first  assumed  that  the  reduction  of  vapor  pressure  at  18° 
was  relatively  the  same  as  at  0°  C.  for  a  given  strength  of  solution.  Further- 
more, that  the  case  of  KCl  would  be  practically  identical  with  the  case  of 
brine.  Afterwards  (using  Landolt  and  Boemstein's  tables)  it  was  found 
that  such  an  assumption  is  inadmissible  and  that  the  equation  should  be 

Table  24. — Air-air  through  KCl  solution  (20.8  grams  in  100  grams  water).  Vessel 
B  (single  tube).  Jl/=37.425  grams;  C=  134.43;  P(,  =  2.47o;  float,  2r  =  3.8  cm.; 
vessel,  2r=5.8  cm.     ptg=  1.1 133  at  24.5°. 


Date. 

Barom- 
eter. 

i 

H 

Vo 

Date. 

Barom- 
eter. 

/ 

// 

Vo 

Sept.  18.. 

76.06 

0 
19.8 

67.32 

15.223 

Oct.     7.. 

75.68 

19.2 

64.78 

14.675 

!9.. 

7585 

21 .2 

66 

54 

'4 

981 

8.. 

76 

34 

19.6 

64.69 

«4 

638 

20.  . 

76.03 

22.0 

66 

26 

'4 

878 

9.. 

76 

78 

21.5 

65.04 

14 

631 

21 .  . 

76.90 

18.8 

65 

33 

"4 

820 

10.  . 

76 

27 

23.0 

65 -37 

'4 

637 

23.. 

76.81 

17.0 

64 

67 

•4 

752 

II .  . 

76 

72 

21.9 

65.17 

'4 

640 

24.. 

77.00 

•7-4 

64 

62 

'4 

718 

12.  . 

76 

40 

22.9 

65.33 

14 

633 

25.. 

76.72 

17.8 

64 

74 

>4 

731 

14.. 

76 

88 

22.6 

65.23 

14 

622 

26.. 

76.54 

17.8 

64 

70 

'4 

722 

15.. 

76 

08 

22.5 

65.  II 

•4 

600 

27.. 

76.31 

17.8 

64 

62 

14 

703 

16.. 

76 

92 

19.8 

64.43 

•4 

570 

28.. 

77  04 

19.2 

64 

95 

M 

7'3 

17.. 

76 

44 

20.4 

64.49 

'4 

556 

30.. 

76.90 

'7-4 

(,4 

94 

«4 

793 

18.. 

76 

3« 

21.6 

64.74 

14 

559 

Oct.      I .  . 

76.03 

18.0 

64 

53 

>4 

674 

19.. 

75 

97 

22.0 

64.84 

14 

561 

2.  . 

76.58 

18.2 

64 

65 

14 

690 

21 .  . 

77 

29 

21  .2 

64.38 

14 

494 

3-- 

76.33 

20.2 

65 

02 

«4 

684 

22.  . 

77 

08 

21.  I 

64.36 

14 

495 

4-- 

76. 10 

22.7 

65 

56 

14 

691 

23.. 

76 

05 

22.4 

64.59 

•4 

486 

5-. 

76.69 

20.8 

65.20 

14.699 

0Z 

m 

[ 

m 

K 

m 

1  ^ 

v^ 

rVj 

-^ 

. 

-^ 

Si" 

■v,. 

"^ 

6^m      Zi      }X(kt.S        8       IS       /8       25 


Fig.  22. — Chart  showing  loss  of  standard  volumes 
of  gas  in  diver  in  lapse  of  days.  Diffusion 
of  air  through  KCl  solution. 

7r'  =  ir(i  —0.086)  for  KCl.  Hence  these  data  for  KCl  in  the  table  must  be 
corrected  before  the  diffusion  coefficients  are  computed,  as  follows :  The 
error  of  tt'  being  8ir'  =  0.029X,  its  effect  on  vo  will  be 

dvo  .  ,  Sir' 

This  correction  is  to  be  supplied  in  the  summary.  For  brine,  by  graphic 
interpolation,  using  either  Dieterici's  or  Smits's  observations,  the  correction 
is  7r'  =  7r  (i  — 0.115),  and  this  is  provisionally  used  in  table  24  and  lig.  22. 


LIQUIDS  AND  AIvUED   EXPERIMENTS. 


69 


The  diffusion  of  air  through  strong  KCl  shows  at  the  outset  a  peculiarly 
rapid  march.  This  is  probably  due  to  the  fact  that,  to  remove  air  bubbles, 
the  water  was  placed  under  a  relatively  high  partial  vacuum.  The  rapid 
diffusion  observed  is  in  correspondence  with  the  restoration  of  a  normal 
amount  of  air  to  the  water.  Thereafter  the  march  of  results  is  fairly 
regular,  apart  from  the  invariable  temperature  fluctuation.  From  a  mean 
line  drawn  through  the  observations,  the  coefficient  of  diffusion  may  be 
found  as  follows : 

t'o  =  0.0072  c.c./day,  or  io*°k  =  0.137 
These  data  are  to  be  converted,  as  stated  above,  by  deducting  bir'/H  of 
their  value  where  H  =  t$  and  7r=i.5,  so  that  5^^  =  0.044/65  which  is 
not  appreciable  in  its  bearing  on  k. 

The  coefficient  is  thus  smaller  than  the  lowest  result  for  air  and  water, 
or  quite  small  as  compared  with  the  normal  datum  for  an  air-and-water 
system.  It  follows,  therefore,  that  the  intermolecular  pores  of  water  are 
quite  effectively  stopped  up  by  the  presence  of  KCl  molecules  between 
them.     Diffusion  proceeds  much  more  slowly. 

It  would  be  an  interesting  inquiry  to  find  how  different  gases  behave  in 
relation  to  this  stoppage;  but  the  work  is  not  yet  advanced  enough  to 
warrant  speculation  on  such  questions.  It  is  obvious,  however,  that  from 
extended  series  of  results  like  the  following,  definite  conclusions  as  to  the 
effect  of  density  of  solution  and  chemical  constitution,  etc.,  on  the  structure 
of  the  molecular  pores  must  eventually  be  reached. 

44.  The  Same,  Continued. — The  solution  was  now  diluted  with  water 
to  about  double  the  above  volume,  showing  the  density  of  p^=  1.063  ^t  23°. 
This  is  equivalent  to  9.9  grams  of  KCl  in  100  grams  of  solution,  or  to  11. o 
grams  of  salt  in  100  grams  of  water.  The  vapor  pressures  are  now  larger, 
7r'  =  ir(i— o.o63)being  the  value  inserted  and  holding  as  above  stated  for  brine . 
The  reduction  to  KCl  requires  tt'  =  ir(i  —0.044),  so  that  the  correction 
5x'  =  o.oi97r  and  in  —{dvJdH)h-K'=  —{vJH)bir',  the  factor  57rVH  =  0.029/ 65 
is  too  small  to  make  its  effect  appreciable.  In  other  respects  the  experi- 
ments were  made  as  above.     Table  25  and  fig.  23  show  the  results. 


Fig.  23. — Chart  showing  loss  of 
standard  volumes  of  gas  in  diver 
in  lapse  of  days.  Diffusion  of 
air  through  KCl  solution. 

If  a  mean  line  is  drawn  through  the  data  as  a  whole,  the  results  are 

fo  =  o.oii5  c.c./day  or  io^°»c  =  o.209 

showing  some  increase  of  k  as  compared  with  the  concentrated  solution 

(io^°K  =  0.137) ;  but  in  relation  to  pure  water  by  no  means  as  large  an  incre- 


70 


THE  DIFFUSION  OF  GASES  THROUGH 


ment  as  would  be  expected  for  a  dilution  to  nearly  half  the  original  strength. 
The  stoppage  effect  of  a  content  of  but  lo  per  cent  of  salt  is  still  pronounced. 

Table  25. — Air-air  through  KCl  solution  (11  grams  in  100  grams  water).    Vessel  B 
(single  tube).     Constants  as  in  table  24.     p„=  1.063  at  23°. 


Date. 

Barom- 
eter. 

t 

H 

r. 

Date. 

1 

j  Barom- 

1    eter. 

t 

H 

t'o 

Oct.   26 

-      75-66 

0 
22.2 

66.20 

16. 150 

Nov.  1 1 

•      76.33 

0 
19.1 

64.36 

15.850 

28 

.  1    76 . 20 

21 . 1 

65.80 

16. 106 

12 

-!     75.83 

19.0 

64 -37 

858 

29 

.      76.58 

20.0 

63.40 

16.063 

>3 

.;    76.17 

19.0 

64 -33 

848 

30 

.      75.80 

21.5 

65.60 

16.039 

14 

.1    75.69 

19.0 

64.27 

833 

Nov.    I 

75.91 

19.6 

65.08 

16.003 

•5 

•1    75.72 

19.0 

64.24 

820 

2 

75.62 

20.3 

65. 12 

15.978 

16 

-!   76.52 

18.9 

64.17 

814 

4 

•      77-33 

17.8 

64. 12 

15.859 

18 

.1   76.26 

18.3 

64.00 

801 

5 

.      76.89 

20.4 

64.72 

15.873 

19 

.i   76.29 

18.0 

63.88 

788 

6 

.      76.82 

22.  ! 

65.20 

15.911 

20 

•    75.97 

17.8 

63.70 

755 

7 

.      76.02 

24.0 

65.58 

15.914 

21 

-    76.31 

17.0 

63.68 

757 

8 

-      75-07 

24.0 

65.64 

15.928 

22 

.    75.94 

17.8 

63.64 

740 

9 

•      75-55 

19.1 

64.56 

15.899 

.    76.08 

17.9 

63.59 

15.722 

45.  The  Same,  Continued. — The  solution  was  now  again  diluted  to 
about  one-half  strength,  thus  showing  about  one-fourth  the  original  con- 
centration, and  the  daily  run  of  results  taken  as  in  table  26  and  fig.  24, 
with  the  same  vessel  and  float  as  before.  The  density  of  solution  was 
Pj^=  1.0295  at  21°,  implying  4.2  grams  in  100  grams  of  solution,  or  4.4  grams 


Table  26.- 

-Air-air  through  KCl  (4.4  grams  in  100  grams  water).    Vessel  B  (single 
tube) .     Constants  as  in  table  24.     Pm,  =  i  .0295  at  2 1  °. 

Date. 

Barom- 
eter. 

t 

H 

t'o 

Date. 

Barom- 
eter. 

/ 

// 

J-'o 

Nov.  25. 

26. 

27. 

29. 

30. 

Dec.    2. 

3- 

4- 

1: 

7- 

74-91 
76.20 
76.38 
76.95 
76.79 
76.60 
76.45 
76.30 
77.06 

75-75 
.      76.14 

0 

17.7 
17.6 

17.5 
17.0 
17.0 
16.9 
16.9 
17. 1 

"7-3 
17.7 
18. 1 

64-74 
64-55 
64-35 
64.03 
63.67 
63.32 
63 -37 
63.41 
63-33 
63-47 
63.47 

16.939 

16.895 

16.849  j 

16.791 

16.697 

16.611 

16.624 

16.623 

16.607 
16.587  1 

1 

Dec.    9. 
10. 
11 . 
12. 
«3- 

\t: 

17- 
18. 
19. 
20. 

76.28 
76.33 

76. 16 
77.10 
76.74 
75-40 
76-45 
76.40 

74-34 
75-88 

0 

18.1 
.8.1 
17.9 

17.9 
17.7 

»7-4 
17-4 

'7-5 
17.8 
17.8 
17.9 

63.49 

63-33 
63.22 
63.10 
62.92 
62.83 
62.64 
62.60 
62.46 
62.34 
62.21 

16.593 
16.551 

«6.533 
16.502 
16.463 
16.457 
16.407 
16.390 
16.340 
16.309 
16.269 

#21_1_„ I. 

,JbpW36  M5      JO 

Fig  .  24 . — Chart  showing  loss  of  stan- 
dard volumes  of  gas  in  diver  in 
lapse  of  days.  Diffusion  of  air 
through  KCl  solution. 


lylQUIDS  AND  Al,LieD  EXPERIMENTS. 


71 


in  100  grams  of  water.  The  vapor  pressure  was  put  7r'  =  7r(i  —0.017).  The 
chart  shows  the  results,  which  are  unfortunately  irregular  for  some  unex- 
plained reason,  there  being  in  the  usual  way  a  very  slow  adjustment  to  the 
equilibrium  conditions,  after  which  the  gas  diffuses  at  a  fairly  regular  rate. 
The  diffusion  constants  are  (vessel  B), 

i'o  =  0.0222  c.c./day  or  io^''/c  =  0.423 

a  reasonable  advance  on  the  former  rates.  The  three  curves  for  KCl  solu- 
tions show  that  not  until  after  the  lapse  of  two  weeks  do  definite  rates 
appear.  These  essentially  final  rates  are  the  ones  taken.  In  each  case 
there  seems  to  be  an  adjustment  of  the  gas  (Oj,  Nj),  which  actually  diffuses, 
to  the  solution. 


46.  The  Same,  Continued. — On  further  dilution  with  about  an  equal 
volume  of  water  the  density  of  the  solution  was  p=i.oi7o  at  21°,  corre- 
sponding to  2.65  grams  in  100  grams  of  solution,  or  2.7  grams  in  100  grams 
of  water.     Thus  the  vapor  pressure  became  7r'  =  7r(i  — o.oio). 

The  progress  of  the  diffusion  is  given  in  table  27  and  fig.  25.  The  latter 
shows  marked  irregularity  at  the  beginning  (as  usual),  but  the  curve  be- 
comes fairly  smooth  when  daily  observations  are  replaced  by  weekly  obser- 
vations. Clearly,  therefore,  the  daily  churning  up  of  the  solution  during 
observation,  usually  at  a  relatively  high  temperature,  is  unfavorable  to  a 
steady  progress  of  results.  The  locus,  however,  is  not  quite  straight,  for 
reasons  which  can  not  be  inferred,  as  temperature  was  fairly  constant. 

Table  27. — Air  into  air  through  KCl  solution  (2.7  grams  in  roo  grams  water).     Con- 
stants as  in  table  24.     Vessel  B.    py,=  1.0170  at  21°. 


Date. 

Barom- 
eter. 

t 

H 

Vo 

Date. 

Barom- 
eter. 

t 

H 

Vo 

Dec.  21 . . 

76.57 

0 
18.0 

65.50   17.484 

Jan.      I . . 

76.01 

0 
18.2 

64.41 

17. 181 

23.. 

76.75 

«7 

8 

65.00   17 

362 

2.  . 

76.87 

18 

3 

64.35 

17. 162 

24.. 

75.70 

"7 

7 

64.87    17 

330 

3.. 

73.98 

18 

4 

64.49 

17.193 

26.. 

77.10 

•7 

^ 

64.47    17 

247 

10.  . 

77.35 

«7 

9 

63.85 

17.050 

28.. 

75.50 

«7 

6 

64.49I  17 

234 

17.. 

76.54 

•7 

6 

63.39 

16.941 

30.. 

75-74 

•7 

7 

64.43  n 

213  i 

24.. 

76. 10 

18 

0 

63. 12 

16.849 

31.. 

76.34 

18.0 

64.37  17.183 

! 

3'.. 

76.17 

18.0 

62.90 

16.790 

iO 


15       XO 


3iec.ZI      26      3/  Jan.5 

Fig.  25. — Chart  showing  loss  of  standard  volumes  of 
gas  in  diver  in  lapse  of  days.  Diffusion  of  air 
through  KCl  solution. 


72 


THe  DIFFUSION  OF  GASES  THROUGH 


The  rates  of  diffusion  are 

i'o  =  o.oi45  c.c./day  or  10^^  =  0.256 

There  has  thus  been  a  retrogression  of  rates,  while  the  other  diffusions  in 
the  same  region  behaved  normally.  The  rate  is  still  far  from  the  large 
value  corresponding  to  pure  water. 

47.  Diffusion  of  Air  Into  Air  Through  NaCl  Solution. — The  experiments 
were  made  in  vessel  F,  the  original  solution  being  nearly  concentrated. 
The  density  was  p„  =  i .  1450  at  22°,  equivalent  to  1 9.6  grams  in  100  grams  of 
solution  or  to  24.4  grams  in  100  grams  of  water.  The  vapor  pressures  were 
taken  as  7r'  =  7r  (i— 0.157). 

The  current  data  are  given  in  table  28  and  fig.  26  a. 

Fig.  26  A  shows  a  fairly  regular  progress  of  results  and  the  constants  are 

i'o  =  0.0035  c.c./day  or  io^°k-  =  0.088 
showing  very  slow  diffusion. 

Table  28. — Air-air  through  brine  (24.4  grams  in  100  grams  water).  Single-tube  vessel. 
M=  10.9387  grams;  C=^g.2g4;  pg=2.466;  float,  2r  =  3.oo  cm.;  vessel,  2r=4.7cm.; 
Pu>=  1.145  at  22°. 


Date. 


Nov.  12 
>3 
14 
15 
16 
18 

>9 
20 
21 
22 
23 
25 
26 

27 

29 

30 

Dec.    2 


Barom- 

eter. 

t 

H 

fo 

75-85 

0 
19.0 

72-95 

4.587 

76.17 

18 

8 

73.09 

4 

599 

75.69 

18 

8 

73.20 

4 

606 

75.72 

18 

8 

73.21 

4 

607 

76.52 

18 

5 

73.12 

4 

606 

76.26 

18 

0 

72.88 

4 

598 

76.29 

«7 

7 

72.79 

4 

596 

75-97 

•7 

7 

72.61 

4 

584 

76.31 

'7 

3 

72-48 

4 

582 

75-94 

•7 

3 

72-43 

4 

579 

76.08 

»7 

5 

72.53 

4 

582 

74.91 

«7 

3 

72.47 

4 

582 

76.20 

«7 

3 

72.40 

4 

577 

76.38 

«7 

I 

72.19 

4 

566 

76.95 

16 

6 

71.96 

4 

559 

76.79 

16 

6 

71.64 

4 

538 

76.60 

16 

4 

71.44 

4 

529 

Date. 


Barom- 
eter. 


Dec. 


76.45 
76.30 
77.06 

75-75 
76.14 
76.28 
76.33 
75-92 
76. 16 
77.10 
76.74 
75-40 
76-45 
76.40 

74-34 

75-88 


t 


H 


6.5 
6.6 


71.48 
71.51 
71.5! 
71.64 
71.63 
71.63 
71-53 
7«-54 
7«-33 
71.27 
71 .26 
71 .  11 
70.94 
70.65 
70.67 
70.65 


t'o 


4-530 
4.530 
4-525 
4.529 
4.522 
4.522 
4.516 

4-523 
4.508 

4-507 
4.509 
4.501 
4.487 
4.467 
4.468 
4-467 


cJilcaiZ      Jr      ZZ      Zia)ecl        7        H       11 


Fig.  26  A,  B. — Chart  showing  loss  of  standard  volumes 
of  gas  in  diver  in  lapse  of  days.  Diffusion  of  air 
through  NaCl  solution. 


LIQUIDS  AND  ALLIED  EXPERIMENTS. 


73 


48.  The  Same,  Continued. — On  dilution  with  about  an  equal  bulk 
of  water  the  density  was  p=  1.0680  at  21°,  corresponding  to  9.5  grams  in 
100  grams  of  solution  or  10.5  grams  in  100  grams  of  water.  The  vapor 
pressure  was  7r'  =  ir(  1—0.060). 

The  record  of  results  is  contained  in  table  29  and  fig.  26  b.  The  march 
of  values  as  a  whole  is  very  regular,  particularly  when  the  daily  observations 
are  replaced  by  weekly  observations.     The  rates  of  diffusion  are 

i'o  =  o.oo725  c.c/day  or  io*°/c  =  o.i92 
showing  a  normal  increase  of  rates  toward  the  value  for  pure  water. 


Table  29. — 

Air  into  air  through  NaCl  solution  (10.5  grams  in  100 

grams 

water). 

Vessel 

F.    Constants  as  in  table  28.     p„=  1.0680  at  21°. 

Date. 

Barom- 
eter. 

t          H 

to 

Date. 

Barom- 
eter. 

t 

H 

fo 

Dec.  21.. 

76.57 

0 
17.5     64 . 60 

4.632 

Jan.      I . . 

76.01 

0 
17.8 

64.00 

4.585 

23.. 

76 

75 

17.4  j  64.46 

4.624 

2.  . 

76.87 

18.0 

63.94 

4-578 

24.. 

75 

70 

17.2  1  64.44 

4.624 

3-- 

73-98 

18. 1 

63.99 

4.580 

26.. 

77 

10 

17. 1  i  64. 12 

4.603 

10. . 

77-35 

17.6 

63.26 

4.534 

28.. 

75 

50 

17. 1 

64.13 

4.604 

17.. 

76.54 

•73 

62.40 

4-477 

30.. 

75 

74 

«7-3 

64.05 

4.596 

24.. 

76. 10 

17.7 

61.82 

4.430 

31.. 

76.34 

17.6 

63.99 

4.587 

31.. 

76.17 

17.7 

61 .  12 

4-379 

49.  Diffusion  of  Air  into  Air  Through  CaCIj  Solution. — This  solution 
was  prepared  by  putting  140  grams  of  approximately  anhydrous  calcic 
chloride  in  400  c.c.  of  water.  Its  density  was  found  to  be  1.1922  at  24.9°  C. 
A  table  of  densities  between  16°  and  25°  was  computed,  as  before.  The 
solution  actually  contained  about  21.4  grams  of  CaCl2  in  100  grams  of 
solution,  or  27.2  grams  of  salt  in  100  grams  of  water.  In  endeavoring  to 
obtain  the  vapor  pressure  it'  above  the  solution,  some  difficulty  was  encoun- 
tered. By  graphic  interpolation  for  the  given  concentration,  the  data  at  0°  C. 
from  Dieterici's  observations  should  be  ir'  =  tt  (i  —  0.198).  The  results  of 
Tammann  made  at  considerably  higher  temperatures  would  give  7r(i  —0.145) 
for  the  same  solution.  The  former  result  was  assumed,  as  the  temperature 
of  observation  was  nearer  0°  C.  The  effect  on  the  diffusion  coefficient  is  of 
no  consequence.     The  daily  observations  are  given  in  table  30  and  fig.  27. 

The  diffusion  of  air  through  strong  solution  of  CaClg  is  not  of  an  abnormal 
character,  except  in  the  temperature  fluctuations.  The  rates  of  diffusion 
(obtained  by  a  mean  line  passed  through  the  observations)  are 

z»Q  =  0.0062  c.c/day  io^°/c  =  o.2i3 

being  again  much  less  than  the  normal  value  for  the  air- water  system. 
The  physical  pores  of  the  liquid  are  thus  virtually  still  much  smaller. 

It  is  important  to  note  that  notwithstanding  the  greater  concentration 
of  the  calcic  chloride  solution,  diffusion  proceeds  more  rapidly  than  for  the 
weaker  solution  of  KCl.  In  other  words,  the  virtual  stoppage  is  much  more 
effective,  cat.  par.,  in  the  case  of  KCl  than  in  the  case  of  CaClj,  as  far  as  can 
yet  be  foreseen.  True,  it  seems  possible  that  all  comparisons  will  have  to 
be  made  with  the  same  apparatus,  as  each  may  have  its  own  constants. 


74 


THE   DIFFUSION   OF  GASES  THROUGH 


Table  30. — Air-air  through  CaCh  solution  (27.2  grams  in  100  grams  water).  Vessel 
C (single  tube).  M=  14.448  grams;  pg  =  2.4S-j;  C=^i.gi;  Pui=  1.1922  at  24.9°;  float, 
2r  =  2.85  cm.;  vessel,  2r  =  4.6  cm. 


Date. 

Barom- 
eter. 

t 

H 

to 

Date. 

Barom- 
eter. 

t 

H 

Vo 

Sept.  19 

•      75-85 

0 
21-5 

70.24 

1 

5-399 

Oct.  7 

.      75-68 

0 
19.2 

67.16 

5.199 

20 

.      76.03 

22.5 

70.47 

401 

8 

-      76-34 

19.8 

67.  12 

187 

21 

.      76.90 

18.8 

69.52 

388 

9 

.      76-78 

21.5 

67-35 

"77 

23 

.      76.81 

17.0 

68.74 

358 

10 

•      76.27 

23.0 

67-54 

168 

24 

.      77.00 

17-4 

68.57 

338 

II 

•      76-72 

21.9 

67.47 

180 

25 

•      76-72 

17.6 

68.51 

330 

12 

.      76.40 

22.8 

67.44 

163 

26 

•      76.54 

17.6 

68.41 

323 

14 

.      76.88 

22.6 

67.28 

5 

•55 

27 

•      76-31 

.7-6 

68.22 

308 

15 

.      76.08 

22.5 

67.21 

151 

28 

•      77-04 

19.0 

68.34 

294  1 

16 

.      76.92 

20.0 

66.58 

141 

30 

76.90 

17-4 

68.03 

296 

«7 

•      76.44 

20.6 

66.56 

131 

Oct.      I 

•      76.03 

18.0 

67-53 

247 

18 

.      76-38 

22.4 

66.90 

^ 

128 

2 

.      76-58 

18.2 

67.44 

236 

•9 

•      75-97 

22.2 

66.82 

125 

3 

•      76-33 

20.5 

68.20 

257 

21 

•      77-29 

21.4 

66.50 

1 12 

4 

76.10 

22.8 

68.  n 

215 

22 

.      77-08 

21.3 

66.41 

107 

5 

.      76.69 

20.8 

67.60 

5.207 

23 

.      76.05 

22.3 

66.58 

105 

54 

^--^ 

-^v^ 

50 

-»-.-»^ 

-^ 

- 

25      28  CdS 


15      /8 


Fig.  27. — Chart  showing  lo.ss  of  standard 
volumes  of  gas  in  diver  in  lapse  of 
days.  Diffusion  of  air  through  CaCl2 
solution. 

Table  31. — Air-air  through  CaCls  solution  (13.9  grams  in  100  grams  water). 
C  (single  tube).     Constants  as  in  table  30.    p,p=  i .  105  at  23°. 


Vessel 


Date. 

Barom- 
eter. 

t 

H 

Vo 

Date. 

Barom- 
eter. 

t 

H 

fo 

Oct.   26.. 

75.66 

0 
22.5 

65.64 

5-797 

Nov.    7.. 

76.02 

0 
24.0 

64.91 

5-707 

28.. 

76.20 

21.3 

65.27 

786 

8.. 

75.07 

23.9 

65.00 

7'7 

29.. 

76.58 

20.2 

64.92 

774 

9.. 

75.55 

19.0 

63  95 

709 

30.. 

75.80 

21-7 

65.09 

763 

II.. 

76.33 

19.0 

63.62 

680 

Nov.     I . . 

75  9' 

19.8 

64.56 

750 

12. . 

75.85 

18.9 

63.59 

679 

2.  . 

75-62 

20.5 

64.60 

741 

13.. 

76.17 

iS.9 

63.48 

669 

4.. 

77-33 

17.8 

63.64 

705 

14.. 

75.69 

IQ.O 

63.42 

5 

662 

5-. 

76.89 

20.5 

64.06 

693 

15.. 

75  72 

19.0 

63.27 

648 

6.. 

76.82 

22.2 

64.52 

5.703 

16.. 

76.52 

18.7 

63.22 

650 

642 

Fig.  28  a,  b. — Chart  showing  loss  of  standard  volumes  of  gas  in  diver  in  lapse  of  days. 
Diffusion  of  air  through  CaCU  solution. 


LIQUIDS  AND  ALLIED  EXPERIMENTS. 


75 


But  the  following  data  for  dilute  solutions  of  CaClg  in  the  same  vessel  will 
exhibit  much  more  striking  anomalies  in  this  respect. 

50.  The  Same,  Continued. — The  preceding  solution,  being  diluted  with 
about  an  equal  bulk  of  water,  showed  a  density  of  1.105  at  23°.  This  is 
equivalent  to  12.2  grams  in  100  grams  of  solution,  or  13.9  grams  in  100 
grams  of  water.  The  vapor  pressures  are  correspondingly  increased  to 
7r'  =  7r(i  —  0.075),  for  which  tables  were  computed.  The  diffusion  results 
are  given  in  table  31  and  fig.  28  a,  the  apparatus  and  equipment  being 
otherwise  the  same.  The  mean  rate  of  diffusion  corresponds  to  the  fol- 
lowing data,  again  adducing  a  small  increase  of  k  as  compared  with  the 
former  solution. 

i'o  =  o.oo72  c.c.,/day  and  io^''k  =  o.352 
The  curve  shows  no  initial  disturbances. 

51.  The  Same,  Continued. — The  solution  was  then  further  diluted  to 
about  one-half,  i.  c,  to  about  one-quarter  of  its  original  strength.  The 
density  found  was  1.058  at  1 8°  C,  which  is  equivalent  to  about  7.1  grams 
CaCl2  in  100  grams  of  solution  or  about  7.6  grams  CaCl2  in  100  grams  of 
water.     The  vapor  pressures  were  therefore  taken  as  7r'  =  7r(i  —0.042). 

The  record  of  results  is  given  in  table  32  and  fig.  28  b. 

Table  32. — Air-air  through  CaCl2  solution  (7.6  grams  in  100  grams  water).     Vessel 
C  (single  tube).     Constants  as  in  table  30.     p„=  1.058  at  18°. 


Date. 

Barom- 
eter. 

t 

H 

Vo 

Date. 

Barom- 
eter. 

/ 

H 

J'o 

Nov.  18.. 

76.26 

0 
18.0 

68.88 

6.673 

Dec.    6 

•      75-75 

0 
17-3 

67.74 

6.577 

19.. 

76.29 

'7 

8 

68.78 

6.668 

7 

■      76 

•4 

•7 

8 

67.77 

6.570 

20. . 

75-97 

>7 

6 

68.65 

6.658 

9 

.      76 

28 

•7 

8 

67.81 

6.574 

21 . . 

76.31 

'7 

3 

68.69 

6.669 

10 

.      76 

33 

•7 

8 

67.76 

6.569 

22. . 

75-94 

>7 

3 

68.70 

6.670 

11 

•      75 

92 

17 

5 

67.64 

6.563 

23.. 

76.08 

•7 

5 

68.66 

6.662 

12 

•      76 

16 

17 

6 

67- 54 

6.551 

25.. 

74-9» 

>7 

5 

68.69 

6.664 

«3 

•      77 

10 

•7 

3 

67.31 

6.535 

26.. 

76.20 

•7 

3 

68.59 

6.659 

14 

•      76 

74 

•7 

0 

67.24 

6.534 

27.. 

76.3.8 

>7 

68.58 

6.662 

16 

•      75 

40 

«7 

0 

67. 10 

6.520 

29.. 

76.95 

16 

7 

68.  d8 

6.660 

17 

.      76 

45 

•7 

2 

66.96 

6.502 

30.. 

76.79 

16 

6 

68.13 

6.628 

18 

.      76 

40 

n 

3 

66.67 

6.473 

Dec.    2 . . 

76.60 

i6 

7 

67.66 

6.580 

•9 

•      74 

34 

»7 

5 

66.79 

6.480 

3-- 

76.45 

16 

5 

67.63 

6.582 

20 

•      75 

88 

•7 

6 

66.65 

6.464 

4-- 

76.30 

16 

7 

67.65 

6.579 

21 

.      76 

57 

•7 

7 

^•^5 

6.462 

5-- 

77.06 

17.0 

67.59 

6.568 

23 

•      76-75 

•7-4 

66.27 

6.432 

The  mean  rate  of  diffusion  would  correspond  to 

i'o  =  0.0067  c.c./day  or  10^  =  0.254 
which  is  actually  smaller  than  the  constant  for  the  half  strength  of  solution. 
The  final  rate,  however,  is 

i'o  =  0.0097  c.c./day  or  io^''k  =  0.368 
a  slight  increase  on  the  preceding  rate.     It  is  probable,  therefore,  that  the 
first  rate  was  obtained  in  the  absence  of  equilibrium  conditions.     The  curve 
shows  marked  initial  disturbances,  there  being  no  effective  diffusion  within 
the  first  ten  days. 


76 


THS  DIFFUSION  OF  GASES  THROUGH 


52.  The  Same,  Continued. — The  preceding  solution  diluted  with  an 
equal  bulk  of  water  showed  the  density  p=  1.0274  at  21°  or  :^.:^  grams  in 
TOO  grams  of  solution,  3.4  grams  in  100  grams  of  water,  corresponding  to 
the  vapor  pressure  7r'  =  7r(i  —0.018). 

The  record  of  results  is  contained  in  table  33  and  fig.  29  and  is  verj'^  pecu- 
liar. Even  apart  from  the  usual  irregularity  at  the  beginning  of  the  obser- 
vation period,  the  curve  continues  to  be  sinuous  after  the  weekly  method  of 
observation  is  introduced.  The  mean  value  is  probably  that  of  pure  water, 
though  the  whole  behavior  is  abnormal.     The  mean  diffusion  rates  are 

i'o  =  0.025  c.c./day  or  io%-  =  0.946 

a  value  even  in  excess  of  the  usual  air  value.     If  the  final  rate  were  taken 
the  diffusion  constants  would  be 

r5  =  o.oi97  c.c./day  or  io\'  =  o.744 

which  is  more  nearly  the  probable  result. 

Table  33. — Air  into  air  through  CaCla  solution  (3.4  grams  in  100  grams  water).    Vessel 
C.     Constants  as  in  table  30.     Pii-=  1.0274  at  21°. 


Date. 

Barom- 
eter. 

i 

H 

Vo 

Date. 

Barom- 
eter, 

t 

// 

I'O 

Dec.  26 . . 

77.10 

0 
17. 1 

67-55 

6.895 

Jan.     3.. 

73-98 

0 
18.2 

67.48 

6.865 

28.. 

75-50 

17.0 

67-55 

6.898 

10.  . 

77-35 

17.7 

66.05 

6.729 

30.. 

75-74 

•7-3 

67. 5» 

6.895 

17.. 

76.54 

17.2 

63 -53 

6.483 

3!.. 

76.34 

17.7 

67-55 

6.882 

24.. 

76. 10 

17.8 

62.01 

6.317 

Jan.      I .  . 

76.01 

17.9 

67.50 

6.874 

31.. 

76.17 

17.9 

60.89 

6.201 

2.  . 

76.87 

18.0 

67.34 

6.855 

an 

--^ 

66 

"" 

64 

\ 

N^ 

B?. 

?-* 

^^ 

^-^ 

cl 

6      5 

/  Jail 

5      i 

1       1 

)      Z 

9       'd 

>       3 

9 

Fig.  29. — Chart  showing  loss  of  standard  volumes 
of  gas  in  diver  in  lapse  of  daj-s.  Diffusion 
of  air  through  CaCla  solution. 

53.  Diffusion  of  Air  into  Air  Through  BaClg  Solution. — The  present 
results  are  to  be  compared  in  series  with  the  calcic  and  strontic  chlorides. 
The  concentrated  solution  of  BaCl2  showed  a  density  of  p^^.  =  i .  1 70  at  20°  C, 
therefore  equivalent  to  17  grams  of  BaClo  in  100  grams  of  solution  or 
20.5  grams  in  100  grams  of  water.  The  vapor  pressure  was  taken  as  tt'  =  tt 
(i  —0.050).     The  results  obtained  are  recorded  in  table  34  and  fig,  30  a. 

A  line  drawn  through  the  observations  gives  the  rates 

i'9  =  0.0077  c.c./day  or  10^^'  =  0.192 
low  values,  in  keeping  with  the  concentrated  solution. 


LIQUIDS  AND  ALLIED  EXPERIMENTS. 


77 


Table  34. — Air-air  through  BaCIj  solution  (20.5  grams  in  100  grams  water).  Single- 
tube  vessel.  il/=7.496o  grams;  C=26.926;  pj  =  2.47o;  p„,=  1.170  at  23°;  float, 
2r  =  3.oo  cm.;  vessel,  2r=4.7  cm. 


Date. 

Barom- 
eter. 

t 

//                Vo 

Date. 

Barom- 
eter. 

t 

H           »o 

Nov.    8.. 

75.07 

0 
24.0 

70.19    2.864 

j 

1  Nov.  16. . 

76.52 

0 
18.7 

67.21 

2.787 

9.. 

75.55 

19.0 

68.90    2.854 

j             18.. 

76.26 

18 

0 

66.59 

2.767 

II. . 

76.33 

19.0 

68.11  !  2.821 

:      «9.. 

76.29 

17 

7 

66.31 

2.758 

12. . 

75.85 

19.0 

67.87     2.811 

1           20. . 

75-97 

>7 

5 

66.09 

2.751 

13.. 

76.17 

19.0 

67.64  i  2.802 

21  .  . 

76.31 

•7 

3 

65.86 

2.743 

14.. 

75.69 

19.0 

67.57     2.799 

22.  . 

75.94 

'7 

4 

65.80 

2.739 

15.. 

75.72 

19.0 

67.27     2.787 

23.. 

76.08 

17.5 

65.69 

2.734 

cm.8 


^^^^ 

t 

^       «        23 


dfci'.25 


lol5t5 


Fig.  30  A,  B. — Chart  showing  loss  of  standard  volumes  of  gas  in  diver  in  lapse  of  dajs. 
Diffusion  of  air  through  BaCI^  solution. 

54.  The  Same,  Continued. — The  solution  was  now  diluted  one-half  and 
tested  in  the  same  vessel.  The  density  was  p„=  1.0886  at  21°,  implying 
about  9.6  grams  in  100  grams  of  solution  or  10.6  grams  in  100  grams  of 
water.  This  corresponds  to  the  vapor  pressure  tt'  =  7r(i  —0.050).  Table  35 
and  fig.  30  b  record  the  results  obtained,  which  are  fairly  regular,  except  at 
the  beginning,  where  the  conditions  of  equilibrium  are  being  slowly 
approached.     The  mean  constants  are 

i'o  =  0.0082  c.c./day  or  10  ^\  =  0.225 

a  slight  increase  on  the  preceding  values,  showing  that  the  effect  of  dilution 
as  usual  is  at  first  not  marked. 


Table  35. — Air-air  through  BaClj  solution  (10.6  grams  in  100  grams  water).    Single 
tube  vessel.     Constants  as  in  table  34.    pjfl=  1.0886  at  21°. 


Date. 

Barom- 
eter. 

t 

H 

Vo 

Date. 

Barom- 
eter. 

t 

H 

»o 

Nov.  25 

•      74-91 

0 
17-3 

67.11 

3.194 

Dec.    9 

.      76.28 

0 
17.8 

64.51 

3.066 

26 

.      76.20 

J7-3 

66.80 

3 

179 

10 

.      76.33 

•7 

8 

64.27 

3.054 

27 

.      76.38 

17. 1 

66.49 

3 

166 

II 

-      75-92 

•7 

5 

64. 12 

3.049 

29 

-      76.95 

16.6 

65.81 

3 

I3« 

12 

.      76. 16 

«7 

6 

63.93 

3.039 

30 

-      76-79 

16.6 

65.16 

3 

107 

•3 

•      77- »o 

•7 

3 

63 -57 

3.025 

Dec,    2 

.      76.60 

.6.5 

64.51 

3 

077 

•4 

-      76.74 

•7 

63.27 

3.013 

3 

•      76-45 

.6.5 

64-53 

3 

078 

16 

.      75.40 

'7 

I 

62.93 

2.996 

4 

.      76-30 

16.7 

64-44 

3 

073 

17 

-      76.45 

•7 

2 

62.77 

2.988 

5 

.      77.06 

17.0 

64.50 

3 

072 

18 

.      76.40 

17 

3 

62.51 

2-975 

6 

.      75.75 

•7-4 

64.60 

3 

073 

19 

-      74-34 

'7 

4 

62.36 

2.967 

7 

.      76.14 

17.8 

64.62 

3.071 

20 

.      75-88 

'7-4 

62.22 

2.960 

78 


THE   DIFFUSION   OF   GASES  THROUGH 


55.  The  Same,  Continued. — The  dilution  of  the  preceding  solution 
with  about  an  equal  bulk  of  water  showed  the  density  p=  1.0435  at  21°,  or 
4.83  grams  in  100  grams  of  solution,  5.1  grams  in  100  grams  of  water,  the 
vapor  pressure  being  7r'  =  7r  (i  —0.0 10). 

The  record  of  results  is  given  in  table  36  and  fig.  31,  and  is  throughout 

reasonably  regular,  particularly  after  the  weekly  period  of  observations 

has  been  installed.     The  diffusion  constants  are 

i'o  =  0.00875  c.c./day  or  io^\'  =  0.244. 

which  is  still  far  removed  from  water. 

Table  36. — Air  into  air  through  BaClj  solution  (5.1  grams  in  100  grams  water).    Single- 
tube  vessel.     Constants  as  in  table  34.     p,i,=  1.0435  at  21°. 


Date. 

Barom- 
eter. 

t 

H 

1-0 

Date. 

Barom- 
eter. 

t 

H 

Vo 

Dec.  21 . . 

76.57 

0 
17-5 

63.39 

3.248 

Jan.    2.. 

76.87 

0 
17.9 

60.07 

3.074 

23.. 

76.75 

«7 

3 

61.70 

3.164 

3-- 

73.98 

18.0 

60. 14 

3-077 

26.. 

1    77.10 

•7 

I 

60.78 

3.118 

10.  . 

77-35 

17-5 

58.58 

3.002 

28.. 

1    75  50 

17 

I 

60.94 

3. 126 

17.. 

76.54 

17.2 

57.16 

2.931 

30.. 

i     75-74 

'7 

3 

60.45 

3.099 

24.. 

76. 10 

17.6 

56.57 

2.898 

31.. 

1     76.34 

•7 

6 

60.37 

3.092 

31.. 

76.17 

17.6 

55-74 

2.855 

Jan.      I . . 

j     76.01 

17 

8 

60.32 

3.088 

Si  Jan.  5 

Fig.  31. — Chart  showing  loss  of  standard  volumes  of 
gas  in  diver  in  lapse  of  days.  Diffusion  of  air  through 
BaCh  solution. 

56.  Diffusion  of  Air  into  Air  Through  K2SO4  Solution. — This  solution 
is  the  first  of  the  sulphates  and  is  to  be  compared  with  sodic  sulphate  and 
possibly  with  the  alums.  The  solution  of  K2SO4  showed  a  density  of  p„  = 
1.065  3^t  23°,  corresponding  therefore  to  8  grams  of  K2SO4  in  100  grams 
of  solution  or  8.7  grams  in  100  grams  of  water.  The  vapor  pressure  was 
taken  as  7r'  =  7r(i  —0.017).     The  results  are  given  in  table  37  and  fig.  32  a. 

A  line  drawn  through  the  observations  corresponds  to  the  following  slope : 
i'o  =  o.oi37  c.c./day  or  io%  =  o.40i 
The  small  effect  is  in  keeping  with  the  essentially  dilute  solution  of  a  not 
very  soluble  salt. 

57.  The  Same,  Continued. — This  solution  of  K2SO4  was  diluted  to 
about  one-half  and  the  resulting  density  found  to  be  1.03 15  at  19°,  which  is 
equivalent  to  4  grams  of  K2SO4  in  100  grams  of  solution  or  4.2  grams  in  100 
grams  of  water.  Hence  the  vapor  pressures  are  7r'  =  7r(i —0.008).  The 
record  of  results  is  given  in  table  38  and  fig.  32  b. 

The  mean  diffusion  rates  correspond  to 

»o  =  0.0100  c.c./day  or  io%  =  o.322 


LIQUIDS  AND  ALLIED   EXPERIMENTS. 


79 


Table  37. — Air-air  through  K.SO«  solution  (8.7  grams  in  100  grams  water).  Single- 
tube  vessel.  ^7  =  8.6430  grams;  C=  31. 046;  p(,  =  2.470;  p„,=  i.o6^  at  23°;  float, 
2r  =  3.o3  cm.;  vessel,  2r=4.7  cm. 


Date. 

Barom- 
eter. 

t 

H 

Vo 

Date. 

Barom- 
eter. 

/ 

H 

I'o 

Nov.    8 

•      75  07 

0 
24.0 

70.90 

3.960 

Nov.  20. . 

75-97 

0 
«7.5 

65.07 

3.707 

9 

■      75-55 

19.0 

69.49 

3 

941 

21 .  . 

76.31 

"7 

3 

64.84 

3.697 

1 1 

•      76.33 

19.0 

68.39 

3 

879 

22.  . 

75-94 

>7 

4 

64.74 

3.690 

12 

.      7585 

19.0 

67.96 

3 

854 

23.. 

76.08 

•7 

5 

64.65 

3.683 

•3 

•      76.17 

19.0 

67.64 

3 

836 

25.. 

74-9' 

«7 

3 

64. 55 

3.680 

"4 

•      7569 

19.0 

67.37 

3 

821 

26.. 

76.20 

•7 

3 

64.22 

3.661 

•5 

.      7572 

19.0 

66.94 

3 

796 

27.. 

76.38 

•7 

63.92 

3.646 

16 

■      76.52 

18.7 

66.57 

3 

779 

29.. 

76.95 

16 

6 

63 -34 

3.619 

18 

.      76.26 

18.0 

65.77 

3 

741 

30.. 

76.79 

16 

6 

62.74 

3-584 

•9 

•      76.29 

17.7 

65.44 

3.726 

3« 


34 


iS       Is       25       28 


Fig.  32  A,  B. — Chart  showing  loss  of  standard  volumes  of  gas  in  diver  in  lapse  of  day. 
Diffusion  of  air  through  K2SO4  solution. 

The  final  diffusions  are  given  by 

1^0  =  0.0120  c.c./day  or  10^^  =  0.388 

Both  data  for  k,  strangely  enough,  correspond  to  a  decrease  of  the  original 

rates  for  a  concentrated  solution.     As  in  many  other  cases  to  be  exemplified, 

the  effect  of  dilution  is  thus  of  a  complicated  nature,  seeing  that  the  pores  of 

a  dilute  solution  may  be  smaller  than  those  of  a  more  concentrated  solution. 

T.\BLE  38. — Air-air  through  KjSOi  solution  (4.2  grams  in  100  grams  water).     Single- 
tube  vessel.     Constants  as  in  table  37.     py,=  1.03 15  at  19°. 


Date. 

Barom- 
eter. 

t 

H 

Vo 

Date. 

Barom- 
eter. 

t 

H 

Vo 

Dec.    2 

.     76.60 

0 
16.5 

69.23 

4.188 

Dec.  13 

•      77- "o 

0 
>7.3 

68.00 

4.104 

3 

•     76.45 

16 

5 

68.95 

4 

171 

•4 

•      76.74 

>7 

I 

67.74 

4.090 

4 

.     76.30 

16 

7 

68.90 

4 

165 

16 

•      7540 

•7 

I 

67.32 

4.065 

5 

.     77.06 

>7 

0 

68.74 

4 

152 

«7 

•      76.45 

>7 

2 

67.07 

4.048 

6 

•      75-75 

•7 

4 

68.86 

4 

•54 

18 

.      76.40 

•7 

3 

66.66 

4.023 

7 

•      76.14 

«7 

8 

68.85 

4 

149 

"9 

•      74.34 

>7 

4 

66.78 

4.029 

9 

.      76.28 

»7 

8 

68.90 

4 

152 

20 

.      75.88 

•7 

4 

66.66 

4.022 

10 

.      76.33 

17 

8 

68.72 

4 

141 

21 

.      76.57 

17 

5 

66.45 

4.007 

II 

•      75.92 

»7 

5 

68.48 

4 

130 

23 

•      76.75 

"7 

3 

65.85 

3-974 

12 

.     76.16 

17.6 

68.16 

4.109 

58.  The  Same,  Continued. — On  further  dilution  with  about  an  equal 
volume  of  water  the  density  was  1.0136  at  20°,  corresponding  to  1.7  grams 
in  100  grams  of  solution,  or  1.7  grams  in  100  grams  of  water.  The  vapor 
pressure  was  7r'  =  7r  (1—0.003). 


8o 


THE   DIFFUSION  OF  GASES  THROUGH 


The  record  of  diflfusion  is  given  in  table  39  and  fig.  33.     It  is  throughout 
nearly  regular  and  corresponds  to  the  rates 

I'o  =  0.0100  c.c./day  or  10^^  =  0.302 

which  is  less  than  the  preceding  case  and  still  far  distant  from  the  value  for 
pure  water.     The  advantage  of  the  weekly  period  of  observations  is  obvious. 

Table  39. — Air  into  air  through  K,S04  solution  (r.ygramsin  100  grams  water).   Single- 
tube  vessel.     Constants  as  in  table  37.     Pu,=  1.0136  at  20°. 


Date. 

Barom- 
eter. 

t 

H 

I'O 

Date. 

Barom- 
eter. 

t 

H 

fo 

Dec.  26. . 

77.10 

0 
17. 1 

69.05 

4.294 

Jan.     3 .  . 

73.98 

0 
18.0 

67.36 

4.178 

28.. 

75  50 

17. 1 

68.35 

4.251 

10.  . 

77-35 

•7-5 

66.01 

4.100 

30.. 

75-74 

«7-3 

67.71 

4.209 

17.. 

76.54 

'7-3 

64.78 

4.027 

31.. 

76 -34 

17.6 

67.60 

4.198 

24.. 

76.10 

17.6 

63.86 

3965 

Jan.      I . . 

76.01 

17.8 

67.49 

4.189 

31.. 

76.17 

17.6 

62.73 

3.895 

2. . 

76.87 

17.9 

67.25 

4.172 

4/ 

-^ 

5-9 

\ 

~~~~~ 

^^ 

X-7 

s>- 

'Mit 

6^     5 

IJan. 

J       / 

9       i 

)      ;' 

0     a 

5      5 

0 

Fig.  33. — Chart  showing  loss  of  standard  volumes 
of  gas  in  diver  in  lapse  of  days.  Diffusion 
of  air  through  K2SO4  solution. 


59.  Diffusion  of  Air  into  Air  Through  Na2S04  Solution. — This  solution 
was  prepared  for  comparison  with  K2SO4,  though  unfortunately  neither 
is  very  soluble.  The  density  of  the  Na2S04  was  found  to  be  p„=  1.1160 
at  20°,  implying  13.7  grams  in  100  grams  of  solution  or  15.9  grams  in 
100  grams  of  water.     The  vapor  pressures  were  taken  as  tt'  =  7r(i  —0.035). 

Table  40. — Air-air  through  NaiS04  solution  (15.9  grams  in  100  grams  water).     Vessel 
E  (single  tube).     Constants  as  in  table  20.     Pu,=  i.i  160  at  20°. 


Date. 


Dec. 


Nov.  25 
26 
27 
29 
30 
2 

3 

4 
5 
6 

7 
9 


Barom- 
eter. 


74-9« 
76.20 
76.38 
76.95 
76.79 
76.60 

76.45 
76.30 
77.06 

75-75 
76.14 
76.28 


•7-3 
'7-3 
17. 1 
16.6 
16.6 
16.4 
16.3 
16.6 
16.9 

»7-3 
17.7 
17.7 


H 

Vo 

68.53 

5.182 

68.52 

181 

68.44 

179 

68.18 

167 

67.81 

139 

67- 53 

121 

67.58 

127 

67.63 

125 

67.56 

116 

67.73 

122 

67.73 

115 

67.70 

5. 113 

Date. 


Dec.  10. . 
II.. 
12. . 
13.. 
14.. 
16.. 
17.. 
18.. 
19.. 
20. . 
21 .  . 
23.  . 


Barom- 
eter. 


76.33 
75  92 
76. 16 
77.10 
76.74 
75-40 
76-45 
76.40 

74-34 
75-88 

76-57 
76-75 


H 


67.65 
67.51 
67.42 
67.23 
67. 12 
66.99 
66.83 
66.67 
66.64 
66.39 
66.24 
65.99 


I'O 


5. in 
5.105 
5.096 
5.085 
5.081 
5-071 
5055 
5.041 

5-037 
5.018 
5.006 
4.992 


LIQUIDS  AND  ALLIED  EXPERIMENTS. 


8x 


Table  40  and  fig.  34  a  record  the  results.     The  diffusion  in  the  main 
proceeds  in  accordance  with 

»o  =  o.oo7o  c.c./day  or  io^°/c  =  o.i68 

and  the  rates  finally  obtained  are 

i'o  =  0.0095  c.c./day  or  10*°^  =  0.229 

The  usual  difficulties  in  relation  to  equilibrium  conditions  assert  themselves 
at  the  outset. 


sTSecT 


«       »  S}ec.^       51  Jafl.5 


Fig.  34  A,  B. — Chart  showing  loss  of  standard  volumes  of  gas  in  diver  in  lapse  of  days. 
Diffusion  of  air  through  Na2S04  solution. 


60.  The  Same,  Continued. — Diluted  with  about  an  equal  bulk  of  water 

the  density  of  the  solution  fell  to  p=  1.0580  at  21°,  corresponding  to  6.32 
grams  in  100  grams  of  solution  or  6.75  grams  in  100  grams  of  water.  The 
vapor  pressure  is  x'  =  7r(i —0.014). 

Table  41. — Air  into  air  through  NajSO*  solution  (6.75  grams  in   100  grams  water). 
Vessel  £.     Constants  as  in  table  40.    Pu,=  1.0580  at  21°. 


Date. 

Barom- 
eter. 

t 

// 

Vo 

Date. 

Barom- 
eter. 

t 

H 

fo 

Dec.  26. . 

77.10 

0 
17.1 

70.46 

5.864 

Jan.      3 . . 

73.98 

0 
17.9 

69.48 

5.767 

28.. 

75  50 

17. 1 

6Q.96 

5.822 

10. . 

77-35 

«7.5 

68.58 

5.701 

30.. 

75-74 

»7-3 

69.70 

5.796 

17.. 

76.54 

17.2 

68.08 

5.664 

31.. 

76.34 

•7-4 

69.68 

5-793 

24.. 

76.10 

17.6 

67.68 

5.624 

Jan.      I . . 

76.01 

17.7 

69.54 

5.776 

3t.. 

76.17 

•7-5 

67.30 

5-594 

2. . 

76.87 

17.8 

69.42 

5.764 

The  observ^atjons  are  given  in  table  41  and  fig.  34  b.  They  are  reasonably 
regular  and  show  that  the  weekly  period  of  observations  is  in  every  way 
preferable  to  the  daily  period.     The  rates  of  diffusion  are 

10  =  0.0065  c.c./day  or  io^°k  =  0.164. 

which  is  still  far  below  the  value  for  pure  water,  in  spite  of  the  dilution  of 
the  solution  in  question. 

61.  Diffusion  of  Air  into  Air  Through  FeClg  Solution. — A  nearly  con- 
centrated solution  of  this  very  soluble  salt  was  prepared,  showing  the  density 
1.25 10  at  22°  and  corresponding  to  27.3  grams  in  100  grams  of  solution,  or 
37.5  grams  in  100  grams  of  water.  A  table  for  the  vapor  pressures  above 
the  solution  could  not  be  fotmd.  The  data  for  CaCl2  were,  therefore,  provi- 
sionally adopted,  as  the  effect  upon  k  is  not  relatively  large,  when  compared 
with  the  other  inevitable  errors.      Hence  the  vapor  pressures  are  tt'  =  x 


82 


THE   DIFFUSION   OF   GASES  THROUGH 


(i  —0.255).  The  curve  obtained  for  the  progress  of  diffusion  is  a  line  nearly 
horizontal,  showing  a  liquid  all  but  impervious  so  far  as  the  air  molecule  is 
concerned.     The  slopes  of  the  curve,  table  42,  fig.  35  a,  correspond  to 

1)0  =  0.00125  c.c./day  or  io^*'/c  =  0.045 

the  smallest  value  thus  far  obtained.  Though  a  comparison  with  AICI3 
is  intended,  it  must  be  remembered  that  the  apparatus  is  the  one  with  the 
long  diver  and  liable  to  show  relatively  small  results. 

Table  42. — Air-air  through  FeCU  solution  (37.5  grams  in  100  grams  water).     Vessel  H 
(single  tube),     p,,  =  1.2510  at  22°.     Constants  as  in  table  23. 


Date. 

Barom- 
eter. 

t 

H 

I'O            i 

Date. 

Barom- 
eter. 

t           H 

I'o 

Dec.    2 

1 

.:      76.60 

0 
•7-5 

67-47 

3.823 

Dec.  16. 

75  40 

0 
•7-9 

67.85 

3.840 

3 

•       76.45 

•7 

3 

67.61 

3-833  ; 

•7- 

76 

45 

•7 

8 

67-77 

3 

837 

4 

.       76.30 

•7 

5 

67-56 

3.828 

18. 

76 

40 

•7 

9 

67.51 

3 

821 

5 

.       77.06 

17 

8 

67.66 

3.830 

19. 

74 

34 

18 

0 

67.72 

3 

831 

6 

•      75-75 

18 

2 

67.78 

3.832 

20. 

75 

88 

18 

2 

67-58 

3 

821 

7 

•      76.14 

18 

6 

67.85 

3.832  ! 

21 . 

76 

57 

18 

I 

67-56 

3 

821 

9 

.      76.28 

18 

6 

67.99 

3.840  : 

23- 

76 

75 

•7 

9 

67.42 

3 

816 

10 

•      76.33 

18 

6 

67-97 

3.838  i 

24- 

75 

70 

•7 

8 

67.42      3 

817 

II 

•      75-92 

18 

2 

68.03 

3.846  i 

26. 

77 

10 

•7 

8 

67.23      3 

806 

12 

.      76.16 

18 

4 

67.99 

3.841 

28. 

75 

50 

•7 

9 

67-36     3 

812 

13 

•      77-10 

18 

0 

67.95 

3-844 

30. 

75 

74 

18 

I 

67.38  I  3 

811 

>4 

•      76-74 

•7-9 

68.06 

3-852 

39 

Skcl 


sf 


B 


4-7  l^ 


Jan.H 


iS       Xi 


Z6 


Fig.  35  A,  B. — Charts  showing  loss  of  standard  volumes  of  gas  in  diver  in  lapse  of  days. 
Diffusion  of  air  through  FeCls  solution. 

62.  The  Same,  Continued. — The  preceding  solution  was  now  diluted 
with  an  equal  bulk  of  water.  The  density  was  thus  reduced  to  1.1260  at 
24°,  corresponding  to  about  14.3  grams  in  100  grams  of  solution  or  16.7 
grams  in  100  grams  of  water.  Thus  the  provisional  vapor  pressures  are 
7r'  =  7r(i  —0.095).     The  record  of  results  is  contained  in  table  43  and  fig.  35  b. 

Table 43. — Air  into  air  through  FeClj  solution  (16.7  grams  in  loo  grams  water). 
Vessel  H.     Constants  as  in  table  42.     Pa,=  1.1260  at  24°. 


Date. 

Barom- 
eter. 

t 

H           V, 

Date. 

Barom- 
eter. 

t 

H 

Vo 

Jan.    11.. 
17.. 

76.28 
76.54 

0 

•7-9 
•7-9 

69.61     4.823 
69.26  j  4.799 

Jan.    24. . 
31.. 

76. 10 
76.17 

0 

18.2 
18.2 

69.00 
68.76 

4-779 
4.762 

The  rates  of  diffusion  correspond  to 

»o  =  0.00275  c.c./day  or  io^*'k  =  0.094 

Observations  were  taken  but  once  a  week  with  an  obvious  advantage 
to  the  smoothness  of  the  curve.     The  ratio  is  here  remarkably  linear. 


LIQUIDS  AND  ALLIED  EXPERIMENTS. 


83 


63.  Diffusion  of  Air  into  Air  Through  AICI3  Solution. — This  is  the 
original  sokition  of  the  series  and  nearly  concentrated,  the  density  being 
p=  1. 1550  at  19°,  corresponding  to  20.2  grams  in  100  grams  of  solution  or 
25.3  grams  in  100  grams  of  water.  The  vapor  pressure,  for  want  of  specific 
data,  was  taken  the  same  as  CaClj  and  is  thus  7r'  =  7r(i  —0.177). 

Table  44. — Air  into  air  through  AlClj  solution  (25.3  grams  in  100  grams  water). 
Vessel  A  (single  tube).     Constants  as  in  table  i6.     Pu;=i.i550  at  19°. 


Date. 

Barom- 
eter. 

t 

H 

»o 

Date. 

Barom- 
eter. 

t 

H 

v» 

Dec.  26.  . 
28.. 
30.. 

31- 

Jan.      I .  . 

2.  . 

77.10 
75-50 
75-74 
76.34 
76.01 
76.87 

0 

17.0 
17.0 
17.2 

'7-5 
17.7 
.7.8 

71.46 
71 .21 
71.38 
71.41 
71.44 
7' -43 

4.921 
4.904 
4.912 
4.910 
4.909 
4.906 

Jan.     3 .  . 
10.  . 
17.. 

24- 
31.. 

73-98 
77-35 
76-54 
76. 10 

76-17 

0 
17.9 

'7-4 
17.1 

'7-4 
'75 

71.25 
70.95 
70.62 

70-45 
70.34 

4.892 
4.879 
4.861 
4.845 
4.836 

SleM      SI  'Jan  5        »        W 


U 


25       50 


D 


Fig.  36. — Chart  showing  loss  of  standard  vol- 
umes of  gas  in  diver  in  lapse  of  days. 
Diffusion  of  air  through  AICI3  solution. 

The  record  of  results  is  contained  in  table  44  and  fig.  36  and  is  largely 
completed  in  weekly  periods.      The  diffusion  is  slow  and 
reasonably  regular,  showing  the  rates 

i>o  =  o.oo225  c.c./day  or  io^*'k  =  o.o76 

a  very  low  value  in  correspondence  with  the  density  of 
solution. 


A 


A 


7y 


r 


Fig 


37- 


64.  Diffusion  of  a  Gas  Through  a  Manometer  Tube. — 

This  method  of  finding  the  coefficient  of  diffusion  is  neces- 
sarily excessively  slow.  It  was  installed  merely  as  a  cor- 
roboration of  the  above  data  for  k,  which  it  was  supposed 
to  reproduce  in  order  of  value. 

In  fig.  37,  ah  is  a  manometer  tube  about  0.6  cm.  internal 
diameter,  closed  at  both  ends  and  containing  about  the 
same  volume  of  air,  ac  and  bd,  at  each  end  of  the  liquid  cb. 
In  this  way  the  effect  of  temperature  is  diminished, 
though  it  is  necessary  to  observe  a  nearly  constant  tem- 
perature, since  the  liquid  invariably  expands. 

This  tube  with  a  thermometer  was  placed  in  a  vault,  to  be  observed  in 
the  lapse  of  years,  more  than  one  of  which  has  since  gone  by.  The  excur- 
sion of  the  two  ends  of  the  liquid  column  are  separately  read  off,  c  rising 
and  b  falling  by  less  than  a  millimeter  in  a  year.  Glass  scales  were  attached 
to  the  shanks  of  the  tube  for  this  purpose. 


Closed 
manometer  ad- 
justed for  diffu- 
sion of  air  through 
water. 


84 


THE  DIFFUSION  OF  GASES  THROUGH 


Table  45  shows  the  results  as  thus  far  obtained. 

To  compute  k,  the  coefficient  of  volume  diffusion,  the  equation  becomes 

K  =  i)/a{dp/dl)  =  h{i  +  2h"'/h")/pg 

where  h  is  the  rise  per  second  of  the  lower  meniscus  and  the  fall  per  second 
of  the  upper,  //'the  head  of  liquid  of  density  p,  2h"'-\-h"  the  total  length  of 
column  through  which  diffusion  takes  place.  The  table  shows  that  on 
the  average  7^  =  26.45  —  26.37  =  0.08  cm.  below,  and  16.27  —  16.20  =  0.07  cm. 
above,  in  about  17^  months,  or  45.6 X 10^  seconds.     Hence 


h  = 


0-075 
46X10' 


1  while  I 


2h' 


h" 


=  i-f 


9-4 


10.2 


and  pg=98i 


Therefore  /c  =  o.o3X  io~^°  nearly,  a  value,  even  in  consideration  of  the  long 
time  of  observation,  17  months,  and  the  small  displacement  of  meniscus, 
surprisingly  below  the  datum  furnished  by  experiments  with  the  Cartesian 
diver  above,  «  =  0.8X10"^°. 

Table  45. — Diffusion  in  U-tube. 


Date. 

t 

Level    Level 
below,  above. 

Diff. 

Date. 

t 

Level    Level 
below. !  above. 

Diff. 

1911. 

0 

1912. 

0 

1 

April  19. . 

18.5 

26.40 

16.20 

10.20 

Oct.     6.. 

19.0 

26.35      16.25 

10.10 

23. . 

15.0 

26.48 

l6.20 

10.28 

24.. 

20.0 

26.38  i  16.28 

10.10 

30.. 

17.0 

26.48 

16.20 

10.28 

Dec.  31.. 

18.5 

26.37     16.27 

10.10 

May    7 . . 

17.8 

26.48 

16.20 

10.28 

28.. 

20.0 

26.42  !  16.22 

10.20 

This  experiment  shows  that,  so  far  as  the  manometer  is  concerned,  the 
diffusion  error  will  be  negligible.  It  is  by  no  means  so,  however,  when  it 
is  a  question  of  storing  a  pure  gas  over  water  in  air. 

Nothing,  however,  has  been  brought  forward  to  suggest  why  this  direct 
result  for  k  with  the  manometer  should  be  but  4  per  cent  of  the  value  found 
by  the  diver,  unless  it  be  the  continual  or  intermittent  churning  up  of 
gradients  by  temperatm-e,  and  by  the  diver  in  the  latter  case  of  wide  tubes, 
as  compared  with  the  fixed  gradients  in  the  narrow  tube  of  the  manometer. 
The  disparity  of  values  is  one  which  can  only  be  settled  in  the  lapse  of  much 
more  time,  inasmuch  as  h  is  as  yet  too  small  to  be  trustworthy.  If  it  takes 
the  divers  nearly  a  month  to  reach  equilibrium  conditions,  it  should  take 
the  manometer  much  longer,  and  the  experience  with  the  long  divers  in 
§41  may  be  recalled.  Any  small  difference  in  the  gas  above  the  two 
meniscuses  of  the  manometer,  produced,  for  instance,  in  closing  the  tube 
with  the  blow-pipe,  would  be  a  serious  consideration  in  case  of  the  small 
amount  of  gas  in  either  shank  of  the  U-tube.  Correlative  experiments 
with  wider  tubes  naturally  suggest  themselves,  and  the  same  have  been 
installed  to  be  read  off  next  year. 


UQUIDS  AND  ALLIED  EXPERIMENTS. 


85 


65.  Summary. — The  data  found  in  the  above  observations  have  been 
summarized  in  table  46,  in  which  the  system  of  gas  and  liquid  under- 
going diffusion  is  specified  in  the  first  column,  the  table  from  which 
the  data  are  derived  in  the  second,  and  the  vessel  in  which  the  experi- 
ments were  made  in  the  third.  The  vessels  A  and  H  were  of  the  double- 
tube  pattern,  the  remainder  being  single-tube  apparatus.  The  latter 
admit  of  much  easier  treatment;  being  much  less  complicated,  they  prob- 
ably lead  to  results  which  are  for  this  reason  more  trustworthy,  particu- 
larly as  every  apparatus  is  eventually  standardized  by  the  results  of  the 
diffusion  of  air  through  pure  water. 

Table  46. — Sununary. 


System. 

Table. 

Vessel. 

cm.*/day. 

io«»o. 

Days. 

h" 

h'" 

a 

IOl«« 

P.  ct.  of 
solution. 

Air-    HiO    -Air 
Hydrogen— HiO— Hydrogen 

22 

18 
20 
J9 
16 
16 
17 
17 
23 

H 

E 

EE 
F 
A 
A 
A 
A 
H 

0.018s 

.0042 

.0232 

.0082 

Mean    .0505 

Final     .0383 

Initial  .0225 

Final     .0072 

.0800 

214 

49.2 
269 

95. S 
585 
443 
260 

84 
926 

36 

20 
34 
42 
50 
13 
37 
37 
38 

7.42 
4.80 
11.40 
4.23 
4.82 
4.82 
5.07 
5. 07 
9-33 

7.42 
10.30 
3-71 
9-93 
6.88 
6.88 
6.78 
6.78 
7.54 

7.3 
71 
7.1 
7.1 
6.8 
6.8 
6.8 
6.8 
7.3 

0.897 

■  374 

.640 

.779 

3.380 

2.560 

1.432 

.463 

3.383 

Air-     KCl    -Air 

24 

B 

.0072 

84 

35 

8.84 

4.47 

I1.3 

.137 

17.2 

Air- ^^ -Air 

25 

B 

.0115 

133 

28 

10.05 

4.30 

II. 3 

.209 

9.9 

Air        ^P       Air 

4 

26 

B 

.0222 

257 

25 

10.18 

4-47 

11.3 

.423 

4.2 

Air ^^L  -Air 

27 

B 

.0145 

167.8 

41 

11.47 

4.12 

II. 3 

.256 

2.7 

Air-    NaCl  -Air 

28 

F 

.0035 

40.6 

38 

12.38 

4-50 

7.1 

.088 

19.6 

Air-  NaCl    _^^ 

29 

F 

.0073 

84 

41 

12.38 

4.36 

7.1 

.192 

9.5 

Air-   CaCIj  -Air 

30 

C 

.0062 

72.3 

35 

9.00 

5.45 

6.4 

.213 

21.4 

Air       CaCh_Ai^ 

31 

c 

.0072 

84 

21 

8.58 

5.62 

6.4 

.352 

12,2 

Air-   each  _^,,        { 

32 
32 

c 
c 

Mean 
Final 

.0067 
.0097 

78.1 
113 

30 
30 

8.99 
8.99 

5.22 
5.22 

6.4 
6.4 

•  254 
.368 

7.1 
7.1 

Air-Caa,.,,        , 

33 
33 

c 
c 

Mean 
Final 

.0250 
.0197 

290 
228 

36 
36 

9.72 
9.72 

5-37 
5.37 

6.4 
6.4 

.946 

.744 

3.3 
3  3 

Air-   BaCh  -Air 

34 

.0077 

89.8 

15 

13.69 

5.04 

7.1 

.192 

17.0 

Air—B^-Air        { 

35 
35 

Max. 

.0082 
.0093 

95.5 
102 

25 
25 

12.90 
12.90 

5. 10 
5.10 

7-1 
7.1 

.225 
.241 

9.6 
9.6 

Air--BfJ?-_Air. 

4 

36 

.0088 

IOI.3 

41 

13. 55 

5.07 

7.1 

.244 

4.8 

Air-  KtSOi  -Air 

37 

__ 

.0137 

159 

22 

12.79 

5.74 

7.2 

.402 

8.0 

Air-K=fO,_Aj,         { 

38 
38 

Mean 
Final 

.0100 
.0120 

116 
140 

18 
18 

11.46 
11.46 

5. 85 
5.85 

7.2 
7.2 

.322 
.388 

4.0 
4.0 

Air      K^SO'-Air 

39 

.0100 

116 

36 

13- 00 

5. 63 

7.2 

.302 

1.7 

Air-  NaiS04  -Air        | 

40 
40 

EE 
EE 

Mean 
Final 

.0070 
.0095 

81 
110 

24 
24 

13. II 
13." 

4.04 
4.04 

7.1 
7-1 

.168 
.229 

13-7 
13.7 

Air-^*fO'-Air 

41 

EE 

.0065 

75.3 

36 

12.83 

3.85 

7.1 

.164 

6.3 

Air-    FeCh  —Air 

42 

H 

.0012 

14.6 

29 

8.70 

7.59 

7.3 

.045 

27.3 

Air-    Pf '  -Air 

43 

H 

.0028 

31.9 

20 

10.44 

7.18 

7.3 

.094 

14-3 

Air-    AlClj   -Air 

44 

A 

.0023 

26.1 

36 

10.80 

6.76 

6.8 

.076 

20.2 

The  fourth  column  contains  the  number  of  cubic  centimeters  lost  by  the 
diver  (by  diffusion)  per  day,  the  fifth  the  corresponding  loss,  Vq,  per  second, 
and  the  sixth  the  duration  of  the  experiment  in  days.  The  quantity 
h"  in  the  seventh  column  shows  the  height  of  the  free  siuface  of  liquid  in 


86  THE   DIFFUSION   OF  GASES  THROUGH 

the  diver  above  its  horizontal  circular  mouth,  the  area  of  which,  a,  is  given 
in  the  eighth  column,  while  h'"  is  the  difference  of  level  of  the  free  surface 
in  the  diver  and  the  free  surface  outside  of  and  above  it,  during  the  occur- 
rence of  diffusion.  The  coefficient  of  diffusion,  i.  e.,  the  number  of  cubic 
centimeters  at  standard  temperature  and  pressure  which  diffuse  across  an 
orthogonal  square  centimeter  per  unit  pressure  gradient,  and  the  per- 
centage of  solute  in  solution  (grams  of  salt  per  loo  grams  of  solution)  are 
contained  in  the  last  two  columns. 

The  cases  of  air  and  of  hydrogen  have  already  been  adequately  discussed 
above  and  the  various  exceptional  values,  particularly  the  case  of  vessel  A , 
interpreted.  The  mean  rate  for  air  may  be  put  /c X  lo^"  =  0.9  and  for  hydro- 
gen (the  value  in  the  present  chapter  is  probably  preferable  because  of 
the  greater  care  taken  to  exclude  air),  kXio^''  =  3.4. 

So  far  as  this  ratio  is  trustworthy,  it  is  not  out  of  proportion  with  the 
ratios  of  mean  molecular  velocities  for  these  gases.  It  is  unfortunate  that 
the  experiments  above  had  to  be  made  with  a  compound  gas  like  air;  but 
the  special  difficulties  involved  in  endeavoring  to  obtain  similar  results 
with  any  simple  gas,  i.  e.,  the  provision  of  an  artificial  atmosphere  in  the 
latter  case,  etc.,  seemed,  at  the  outset  at  least,  to  more  than  counterbalance 
the  advantages  of  a  single  gas.  Whether  this  adoption  was  actually  a 
wise  step  or  not  will  appear  in  the  future.  It  would  not  be  so  difficult  to 
work  with  hydrogen  if  a  region  of  constant  temperature  sufficiently  large 
to  contain  all  apparatus,  including  the  air  pump  and  the  observer,  were 
available;  but  this  has  not  been  the  case.  A  thermostat  for  such  a  purpose 
would  not  only  have  to  be  large  but  would  have  to  be  free  from  breakdown 
for  years.  At  the  beginning  of  the  experiments  much  time  {i.  e.,  several 
weeks)  must  be  allowed  before  a  definite  rate  of  diffusion  can  be  said  to 
appear;  but  a  steady  condition  eventually  presents  itself,  beginning,  as  a 
rule,  abruptly,  and  it  is  not  impossible  that  different  liquids  select  differently 
constituted  gases  for  final  diffusion.  Such  a  gas  may  be  richer  or  poorer 
in  oxygen  than  ordinary  air. 

The  use  of  distilled  water,  which  is  usually  inadequately  aerated,  as  well 
as  the  use  of  tap  water  otherwise  pure,  are  in  this  respect  objectionable; 
for  the  former  will  contain  a  deficiency  and  the  latter  an  excess  of  air. 
Any  change  of  the  gases  in  the  room,  as  produced,  for  instance,  by  gas- 
burners  or  by  hydrocarbon  vapors  or  even  by  decay,  is  to  be  looked  at  with 
apprehension.  In  this  presence  the  partial  pressure  of  the  exceptional  gas 
is  zero  within  the  diver  and  the  gradient  is  at  once  brought  to  bear  at  its 
maximum  value.  When  gas  has  been  dissolved  in  a  liquid  under  pressure, 
the  growth  of  bubbles  on  rough  objects  may  be  noticed  long  after  a  ten- 
dency to  effervesce  has  completely  vanished,  so  that  in  all  cases  fresh  solu- 
tions seem  to  require  a  long  time  to  reach  a  normal  content  of  gas.  The 
composition  of  a  mixture  is  usually  different  in  solution  and  out  of  it.  In 
this  respect  also  the  temperature  variation  and  the  solubility  of  a  gas  are 
menacing;  for  if  the  gas  were  merely  added  to  or  deducted  from  the  gas- 


LIQUIDS  AND  AUAHD  UXPRRIMENTS. 


87 


content  of  the  diver,  the  result  would  be  nil  in  the  lapse  of  time,  supposing 
there  is  no  continuous  mean  rise  or  fall  of  temperature,  the  latter  in  its 
effects  being  indistinguishable  from  diffusion.  The  issue  in  question, 
however,  is  the  change  of  composition  of  the  imprisoned  air,  which  becomes 
either  relatively  rich  or  poor  in  oxygen;  and  this  modifies  the  gradients 
correspondingly.  Any  change  of  barometric  pressure,  moreover,  is  felt  in 
the  gas  inside  and  outside  of  the  diver  at  once,  but  it  does  not  follow  that 
it  is  also  felt  in  the  pores  of  the  liquid.  There  will  probably  be  diffusion 
out  of  and  into  the  pores  of  the  liquid  as  the  barometer  falls  and  rises, 
respectively,  at  a  slow  rate  and  thus  not  easily  observable.  The  presence, 
finally,  of  any  absorbent  of  a  gas  within  the  liquid,  as,  for  instance,  the  case 
of  bright  copper,  may  confuse  the  result. 

Finally,  the  discrepancy  between  the  results  obtained  in  a  closed  manom- 
eter in  the  lapse  of  years  and  the  above  results  with  the  diver  in  the  lapse 


Fio.  38. — Chart  showing  variation  of  volume  coefficients  of 
diffusion  at  standard  pressure  and  temperature  with 
composition  and  density  of  solution. 

of  months  must  be  considered.  These  experiments  have  been  in  progress 
for  so  short  a  time,  relatively  speaking,  that  all  interpretation  is  merely 
tentative.  It  would  not  be  consistent  if  carried  into  detail.  Nevertheless, 
if  we  suppose  the  gas  contained  in  the  pores  of  a  liquid  to  be  relatively  fixed, 
then  the  presence  of  convection  currents  due  to  gradual  changes  of  temper- 
ature on  the  outside  of  the  apparatus  would  carry  the  more  compressed  gas 
of  the  lower  level  to  the  free  surface,  and  conversely.  Such  an  effect,  which 
is  equivalent  to  an  increase  of  gradient,  being  absent  in  the  narrow  tube  of 
the  manometer,  diffusion  should  be  slower  in  the  latter  case,  as  it  appears 
to  be.  Here,  however,  the  identity  of  the  small  amount  of  gas  in  the  two 
shanks  of  the  U-tube  is  in  question. 

If  the  results  of  table  46  be  graphically  represented  for  each  solution,  so 
that  the  coefficient  of  diffusion  may  appear  in  its  variation  with  the  strength 
of  solution,  the  sets  of  curves  given  in  fig.  38  will  exhibit  the  chief  content 
of  the  table.     From  these  curves  it  appears  that  the  diffusion  of  a  gas  in 


88  THE   DIFFUSION   OF   GASBS. 

general  decreases  rapidly  with  the  strength  of  the  solution,  i.  e.,  the  physical 
pores  of  the  solvent  are  invariably  at  least  virtually  stopped  up  by  the 
solute.  But  the  decrease  of  diffusivity  k  occurs  at  a  rapidly  retarded  rate 
with  the  strength  of  solution,  so  that  the  chief  effect  is  already  patent  for 
solutions  l5dng  within  5  to  10  per  cent  strength.  The  water  of  the  solvent 
should  therefore  be  very  pure. 

Different  solutions,  moreover,  behave  quite  differently.  Thus  the  al- 
kalis KCl  and  NaCl  are  more  powerful  in  decreasing  the  diffusivity  of  a  gas 
than  the  chlorides  or  alkaline  earths  BaClg  and  CaCU,  at  least  so  far  as  the  data 
now  available  allow  an  assertion.  One  would  naturally  anticipate  some 
result  here  with  a  bearing  on  the  periodic  law,  but  the  time  for  this  is  not 
yet  at  hand,  and  the  conditions  are  liable  to  be  variously  complicated. 
Thus  the  continued  dilution  of  a  concentrated  solution  does  not  necessarily 
imply  the  continued  decrease  of  the  diffusivity  of  the  gas  through  it.  The 
table  shows  instances,  e.  g.,  CaClj,  K2SO4,  in  which  the  dilute  solutions 
show  lower  diffusion  coefficients  than  the  more  concentrated  solutions. 
One  would  naturally  attribute  such  a  result  (if  indefinitely  substantiated), 
to  the  formation  of  hydrates  at  different  favorable  strengths  of  solution,  by 
which  the  structure  of  the  solution  is  fundamentally  modified. 

In  conclusion,  therefore,  the  present  experiments,  in  spite  of  all  the  labor 
and  patience  spent  upon  them,  have  done  no  more  than  enhance  the  interest 
of  the  subject  in  a  very  real  degree.  That  the  internal  structure  of  the 
liquid  may  in  a  measure  be  explored  in  this  way  admits  of  no  doubt ;  but 
the  path  of  the  explorer  has  proved  very  much  more  arduous  than  the 
initial  trials  promised.  The  work  will  nevertheless  be  continued  in  various 
directions. 


UNIVERSITY    OF    CALIFORNIA 
BRANCH    OF    THE    COLLEGE    OF    AGRICULTURE 

THIS  BOOK  IS  DUil  ON  THE  LAST  DATE 
STAMPED  BELOW 

JA  30 '58^/? 

„n     'CO  "^■5'? 

i8SEP"6l  LU 

I  9SEP  '61  LU 

5  5o  ia 

5m-8,'26 

i 

4913 


Barus 


The  diffusion  of  gases 
through  llqjilda  and  allied 
experiment a 


^B3 


JA  ^0  '58 


]UL  VS^ 


/p.    f£feQQ 


JB3 


LIBRARY,  BRANCH  OF  THE  COLLEGE  OF  AGRICULTURE 


i! 


p 

it^^  i 

17 


i;ii|:;; 


m 


